Relevant bibliographies by topics / Invariant ellipsoid method

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  2. Dissertations / Theses
  3. Conference papers

Academic literature on the topic 'Invariant ellipsoid method'

Author: Grafiati
Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Invariant ellipsoid method"

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O’Dell, Brian D., and Eduardo A. Misawa. "Semi-Ellipsoidal Controlled Invariant Sets for Constrained Linear Systems." Journal of Dynamic Systems, Measurement, and Control 124, no. 1 (April 17, 2000): 98–103. http://dx.doi.org/10.1115/1.1434269.

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This paper investigates an alternative approximation to the maximal viability set for linear systems with constrained states and input. Current ellipsoidal and polyhedral approximations are either too conservative or too complex for many applications. As the primary contribution, it is shown that the intersection of a controlled invariant ellipsoid and a set of state constraints (referred to as a semi-ellipsoidal set) is itself controlled invariant under certain conditions. The proposed semi-ellipsoidal approach is less conservative than the ellipsoidal method but simpler than the polyhedral method. Two examples serve as proof-of-concept of the approach.
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Furtat, I. B., P. A. Gushchin, and A. A. Peregudin. "Disturbance Attenuation with Minimization of Ellipsoids Restricting Phase Trajectories in Transition and Steady State." Mekhatronika, Avtomatizatsiya, Upravlenie 21, no. 4 (April 11, 2020): 195–99. http://dx.doi.org/10.17587/mau.21.195-199.

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Abstract A new method for attenuation of external unknown bounded disturbances in linear dynamical systems with known parameters is proposed. In contrast to the well known results, the developed static control law ensures that the phase trajectories of the system are located in an ellipsoid, which is close enough to the ball in which the initial conditions are located, as well as provides the best control accuracy in the steady state. To solve the problem, the method of Lyapunov functions and the technique of linear matrix inequalities are used. The linear matrix inequalities allow one to find optimal controller. In addition to the solvability of linear matrix inequalities, a matrix search scheme is proposed that provides the smallest ellipsoid in transition mode and steady state with a small error. The proposed control scheme extends to control linear systems under conditions of large disturbances, for the attenuation of which the integral control law is used. Comparative examples of the proposed method and the method of invariant ellipsoids are given. It is shown that under certain conditions the phase trajectories of a closed-loop system obtained on the basis of the invariant ellipsoid method are close to the boundaries of the smallest ellipsoid for the transition mode, while the obtained control law guarantees the convergence of phase trajectories to the smallest ellipsoid in the steady state.
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Fedele, Giuseppe. "Invariant Ellipsoids Method for Chaos Synchronization in a Class of Chaotic Systems." International Journal of Robotics and Control Systems 2, no. 1 (January 28, 2022): 57–66. http://dx.doi.org/10.31763/ijrcs.v2i1.533.

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This paper presents an invariant sets approach for chaos synchronization in a class of master-slave chaotic systems affected by bounded perturbations. The method provides the optimal state-feedback gain in terms of the minimal ellipsoid that guarantees minimum synchronization error bound. The problem of finding the optimal invariant ellipsoid is formulated in terms of a semi-definite programming problem that can be easily solved using various simulation and calculus tools. The effectiveness of the proposed criterion is illustrated by numerical simulations on the synchronization of Chua's systems.
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Tan, Chun Kiat, Jianliang Wang, Yew Chai Paw, and Fang Liao. "Autonomous ship deck landing of a quadrotor using invariant ellipsoid method." IEEE Transactions on Aerospace and Electronic Systems 52, no. 2 (April 2016): 891–903. http://dx.doi.org/10.1109/taes.2015.140850.

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LIU, YANQING, and FEI LIU. "FEEDBACK PREDICTIVE CONTROL OF NONHOMOGENEOUS MARKOV JUMP SYSTEMS WITH NONSYMMETRIC CONSTRAINTS." ANZIAM Journal 56, no. 2 (October 2014): 138–49. http://dx.doi.org/10.1017/s1446181114000315.

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AbstractWe consider feedback predictive control of a discrete nonhomogeneous Markov jump system with nonsymmetric constraints. The probability transition of the Markov chain is modelled as a time-varying polytope. An ellipsoid set is utilized to construct an invariant set in the predictive controller design. However, when the constraints are nonsymmetric, this method leads to results which are over conserved due to the geometric characteristics of the ellipsoid set. Thus, a polyhedral invariant set is applied to enlarge the initial feasible area. The results obtained are for a more general class of dynamical systems, and the feasibility region is significantly enlarged. A numerical example is presented to illustrate the advantage of the proposed method.
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Vrazhevsky, S. A., J. V. Chugina, I. B. Furtat, and D. E. Konovalov. "Optimization of Invariant Ellipsoid Technique for Sparse Controllers Design." Mekhatronika, Avtomatizatsiya, Upravlenie 23, no. 1 (January 18, 2022): 3–12. http://dx.doi.org/10.17587/mau.23.3-12.

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The paper deals with the method for the design of linear controllers with sparse state feedback matrices for control the plants under conditions of unknown and bounded disturbances. The importance of the sparsity property in feedback can be explained by two factors. First, by minimizing the columnar norm of the feedback matrix in the control it becomes pos- sible to use a minimum number of measuring devices. Secondly, by minimizing the row norm of the feedback matrix, the required number of executive (control) devices is minimized. Both properties, if they are achievable in the synthesis of the controller, reduce the cost of the system and improve the fault tolerance and quality of regulation by reducing the structural complexity. The search algorithm for sparse matrices is based on the method of invariant ellipsoids and is formulated as a solution to a system of linear matrix inequalities with additional constraints. A special set of optimization conditions is proposed which for a disturbed system minimizes overshoot and overshoots in transient processes of the disturbed closed- loop system simultaneously with minimizing errors in the steady state. The proposed method also assumes the possibility of minimizing both the row norm of the feedback matrix and the column one, while preserving the robustness properties, which makes it possible to solve the sparse control problem (a sparse control is understood as a linear controller with a sparse feedback matrix). The efficiency of the proposed control scheme is confirmed by the results of computer modeling and comparison with some existing ones.
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Mendelson, Shahar. "Approximating the covariance ellipsoid." Communications in Contemporary Mathematics 22, no. 08 (January 30, 2020): 1950089. http://dx.doi.org/10.1142/s0219199719500895.

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We explore ways in which the covariance ellipsoid [Formula: see text] of a centered random vector [Formula: see text] in [Formula: see text] can be approximated by a simple set. The data one is given for constructing the approximating set is [Formula: see text] that are independent and distributed as [Formula: see text]. We present a general method that can be used to construct such approximations and implement it for two types of approximating sets. We first construct a set [Formula: see text] defined by a union of intersections of slabs [Formula: see text] (and therefore [Formula: see text] is actually the output of a simple neural network). We show that under minimal assumptions on [Formula: see text] (e.g. [Formula: see text] can be heavy-tailed) it suffices that [Formula: see text] to ensure that [Formula: see text]. In some cases (e.g. if [Formula: see text] is rotation invariant and has marginals that are well behaved in some weak sense), a smaller sample size suffices: [Formula: see text]. We then show that if the slabs are replaced by well-chosen ellipsoids, the same degree of approximation is true when [Formula: see text]. The construction is based on the small-ball method.
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Juarez, Raymundo, Vadim Azhmyakov, A. Tadeo Espinoza, and Francisco G. Salas. "An implicit class of continuous dynamical system with data-sample outputs: a robust approach." IMA Journal of Mathematical Control and Information 37, no. 2 (May 21, 2019): 589–606. http://dx.doi.org/10.1093/imamci/dnz015.

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Abstract This paper addresses the problem of robust control for a class of nonlinear dynamical systems in the continuous time domain. We deal with nonlinear models described by differential-algebraic equations (DAEs) in the presence of bounded uncertainties. The full model of the control system under consideration is completed by linear sampling-type outputs. The linear feedback control design proposed in this manuscript is created by application of an extended version of the conventional invariant ellipsoid method. Moreover, we also apply some specific Lyapunov-based descriptor techniques from the stability theory of continuous systems. The above combination of the modified invariant ellipsoid approach and descriptor method makes it possible to obtain the robustness of the designed control and to establish some well-known stability properties of dynamical systems under consideration. Finally, the applicability of the proposed method is illustrated by a computational example. A brief discussion on the main implementation issue is also included.
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Polyakov, Andrey, and Alex Poznyak. "Invariant ellipsoid method for minimization of unmatched disturbances effects in sliding mode control." Automatica 47, no. 7 (July 2011): 1450–54. http://dx.doi.org/10.1016/j.automatica.2011.02.013.

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Juárez, R., V. Azhmyakov, and A. Poznyak. "Practical Stability of Control Processes Governed by Semiexplicit DAEs." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/675408.

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This paper deals with a new approach to robust control design for a class of nonlinearly affine control systems. The dynamical models under consideration are described by a special class of structured implicit differential equations called semi-explicit differential-algebraic equations (of index one), in the presence of additive bounded uncertainties. The proposed robust feedback design procedure is based on an extended version of the classical invariant ellipsoid technique that we call the Attractive Ellipsoid (AE) method. The theoretic schemes elaborated in our contribution are illustrated by a simple computational example.
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Dissertations / Theses on the topic "Invariant ellipsoid method"

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Нікульченко, Артем Олександрович. "Методи та інформаційна технологія децентралізованого гарантуючого керування запасами у мережах поставок з невизначеними запізнюваннями." Thesis, Національний технічний університет "Харківський політехнічний інститут", 2018. http://repository.kpi.kharkov.ua/handle/KhPI-Press/38791.

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Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.13.06 – інформаційні технології. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2018 р. Дисертацію присвячено розробці методів та інформаційної технології (ІТ) децентралізованого керування запасами в мережах поставок (МП) при наявності невизначених запізнювань. Виконано аналіз сучасних інформаційних технологій керування МП. Розроблено математичну модель процесу керування запасами локального вузла МП та її дескрипторне перетворення. Закон керування побудовано у вигляді лінійного зворотного зв'язку за станом. Запропоновано розвиток методу інваріантних еліпсоїдів на основі побудови функціонала Ляпунова-Красовського. За допомогою техніки лінійних матричних нерівностей задачу синтезу регулятора зведено до задачі напіввизначеного програмування. Удосконалено метод прогнозування попиту на ресурси на основі побудови вектора кривої продажів. Запропонований підхід забезпечує оптимальне подавлення впливу зовнішнього попиту на рівні запасів ресурсів за обраним критерієм, а також гарантоване значення показника якості керування. Удосконалено метод визначення максимальної граничної величини запізнювання. Виконано аналіз стійкості керованої МП. Розроблено стратегію реалізації запропонованої ІТ, а також діаграму компонентів інформаційної системи. Результати впроваджено в промислових компаніях та у навчальний процес НТУ "ХПІ".
The dissertation for a candidate degree of technical sciences, specialty 05.13.06 – Information Technologies. – The National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2018. The thesis focuses on the development of methods and information technology (IT) of decentralized guaranteed inventory control in supply networks (SN) with uncertain transportation delays. Modern information technologies of SN control are analyzed. The mathematical model of the inventory control process at a local node of the SN and descriptor transformation of the model have been suggested. The control law is formulated in the form of linear state feedback. The work suggests an extension of the invariant ellipsoid method based on building of the Lyapunov-Krasovskii functional. Controller synthesis problem has been represented as the semidefinite programming problem. Suggested improvements to the method of forecasting the consumer demand for physical resources based on building a sales curve vectors. The suggested approach ensures optimal compensation of external demand influence on the level of resource stocks by the defined criteria. Suggested approach also ensures guaranteed value of the local quadratic control cost. Suggested improvements to the method of determining the maximum allowed delay. Using the comparison method and Lyapunov vector functions, the stability of the managed SN is analyzed. The thesis also provides implementation strategy for the suggested IT, as well as the diagram of the IT components. The results have been used by commercial companies, as well as in the educational process at the National Technical University "KhPI".
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Нікульченко, Артем Олександрович. "Методи та інформаційна технологія децентралізованого гарантуючого керування запасами у мережах поставок з невизначеними запізнюваннями." Thesis, Національний технічний університет "Харківський політехнічний інститут", 2018. http://repository.kpi.kharkov.ua/handle/KhPI-Press/38702.

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Дисертація на здобуття наукового ступеня кандидата технічних наук за спеціальністю 05.13.06 – інформаційні технології. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2018 р. Дисертацію присвячено розробці методів та інформаційної технології (ІТ) децентралізованого керування запасами в мережах поставок (МП) при наявності невизначених запізнювань. Виконано аналіз сучасних інформаційних технологій керування МП. Розроблено математичну модель процесу керування запасами локального вузла МП та її дескрипторне перетворення. Закон керування побудовано у вигляді лінійного зворотного зв'язку за станом. Запропоновано розвиток методу інваріантних еліпсоїдів на основі побудови функціонала Ляпунова-Красовського. За допомогою техніки лінійних матричних нерівностей задачу синтезу регулятора зведено до задачі напіввизначеного програмування. Удосконалено метод прогнозування попиту на ресурси на основі побудови вектора кривої продажів. Запропонований підхід забезпечує оптимальне подавлення впливу зовнішнього попиту на рівні запасів ресурсів за обраним критерієм, а також гарантоване значення показника якості керування. Удосконалено метод визначення максимальної граничної величини запізнювання. Виконано аналіз стійкості керованої МП. Розроблено стратегію реалізації запропонованої ІТ, а також діаграму компонентів інформаційної системи. Результати впроваджено в промислових компаніях та у навчальний процес НТУ "ХПІ".
The dissertation for a candidate degree of technical sciences, specialty 05.13.06 – Information Technologies. – The National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2018. The thesis focuses on the development of methods and information technology (IT) of decentralized guaranteed inventory control in supply networks (SN) with uncertain transportation delays. Modern information technologies of SN control are analyzed. The mathematical model of the inventory control process at a local node of the SN and descriptor transformation of the model have been suggested. The control law is formulated in the form of linear state feedback. The work suggests an extension of the invariant ellipsoid method based on building of the Lyapunov-Krasovskii functional. Controller synthesis problem has been represented as the semidefinite programming problem. Suggested improvements to the method of forecasting the consumer demand for physical resources based on building a sales curve vectors. The suggested approach ensures optimal compensation of external demand influence on the level of resource stocks by the defined criteria. Suggested approach also ensures guaranteed value of the local quadratic control cost. Suggested improvements to the method of determining the maximum allowed delay. Using the comparison method and Lyapunov vector functions, the stability of the managed SN is analyzed. The thesis also provides implementation strategy for the suggested IT, as well as the diagram of the IT components. The results have been used by commercial companies, as well as in the educational process at the National Technical University "KhPI".
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Дорофеев, Юрий Иванович. "Робастное управление запасами в сетях поставок в условиях неопределенности спроса и транспортных запаздываний." Thesis, НТУ "ХПИ", 2016. http://repository.kpi.kharkov.ua/handle/KhPI-Press/21967.

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Диссертация на соискание ученой степени доктора технических наук по специальности 05.13.07 – автоматизация процессов управления. – Национальный технический университет "Харьковский политехнический институт", Харьков, 2016 г. Диссертация посвящена обоснованию и разработке концепции и методов синтеза автоматизированных систем робастного управления запасами в сетях поставок в условиях неопределенности спроса и транспортных запаздываний на основе развития метода инвариантных эллипсоидов с использованием дескрипторного подхода и параметризованной функции Ляпунова. Построена математическая модель сети поставок как объекта автоматического управления в условиях неопределенного, но ограниченного спроса с учетом транспортных запаздываний и несимметричных ограничений на уровни запасов и объемы заказов ресурсов. С целью учета неопределенности значений интервалов транспортных запаздываний обоснована необходимость использования матрицы динамики с параметрической неопределенностью аффинного типа. В результате получена дискретная динамическая модель в пространстве состояний, область неопределенности, которой представлена выпуклым многогранным множеством. Сформулированы необходимые и достаточные условия существования допустимого управления для задачи синтеза ограниченного робастного гарантирующего управления запасами в сетях поставок. Задача оценивания допустимой области в пространстве управляющих воздействий представлена в виде системы билинейных матричных неравенств, для решения которой предложен итерационный алгоритм. Задача вычисления значений весовых матриц, определяющих квадратичный критерий качества управления, при которых обеспечивается минимальный размер инвариантного эллипсоида замкнутой системы, сведена к задаче разрешимости системы билинейных матричных неравенств, для решения которой предложен итерационный алгоритм. Построена математическая модель системы подачи и распределения воды как объекта автоматического управления в виде совокупности линейных подсистем управления запасами воды отдельных секторов потребления с нелинейными взаимосвязями при условии существования квадратичных ограничений на их значения. Решена задача автоматизации управления режимами работы насосных станций в системе централизованного водоснабжения населенного пункта, которая сведена к последовательности задач полуопределенного программирования, решаемых численно в реальном времени.
The dissertation for the degree of doctor of technical sciences, specialty 05.13.07 – automation of control processes. – The National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2016. The dissertation is devoted to the development of a concept and synthesis methods of automated systems of robust inventory control in supply networks with uncertainty of demand and time-delays on the basis of extension of the invariant ellipsoids method using the descriptor system approach and parameter-dependent Lyapunov function. A discrete mathematical model in state space of supply network is developed, which has parametric uncertainty of affine type. The control law is based on the periodic inspection of resources stock levels and constructed in the form of a linear dynamic feedback with respect to deviation between cash and safety stock levels of resources. In order to suppress the influence of the changes in external demand while ensuring robust stability of a closed system the invariant ellipsoids method is used, which reduces the synthesis of optimal controller to a problem of the search for the smallest invariant ellipsoid of the closed system. Using linear matrix inequalities the controller synthesis problem is reduced to a sequence of semidefinite programming problems, that are solved numerically in real time. A descriptor system approach with parameter-dependent Lyapunov function is used to reduce the degree of conservatism of control results. A necessary and sufficient conditions of the control existence for a constrained robust guaranteeing inventory control synthesis problem in supply networks are formulated. A problem of estimating the allowable region in the space of control actions is formulated in terms of solvability of bilinear matrix inequalities system, for solution of which an iterative algorithm is proposed. A mathematical model of the water distribution system as an automatic control object in the form of a set of linear subsystems with nonlinear relationships under condition of the existence of a quadratic constraints on their values is developed. A problem of pumping stations modes control automation in the centralized water supply system is solved.
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Дорофєєв, Юрій Іванович. "Робастне керування запасами у мережах поставок в умовах невизначеності попиту та транспортних запізнень." Thesis, НТУ "ХПІ", 2016. http://repository.kpi.kharkov.ua/handle/KhPI-Press/21964.

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Дисертація на здобуття наукового ступеня доктора технічних наук за спеціальністю 05.13.07 – автоматизація процесів керування. – Національний технічний університет "Харківський політехнічний інститут", Харків, 2016 р. Дисертація присвячена обґрунтуванню та розробці концепції та методів синтезу автоматизованих систем робастного керування запасами в мережах поставок на основі розвитку методу інваріантних еліпсоїдів з використанням дескрипторного підходу і параметризованої функції Ляпунова. Розроблено дискретну математичну модель керованої мережі поставок у просторі станів з використанням матриці динаміки, яка має параметричну невизначеність афінного типу. Закон керування побудовано на основі періодичної перевірки рівнів запасів ресурсів у вигляді лінійного динамічного зворотного зв'язку за сигналом нев'язки між готівковими і страховими рівнями запасів. Для подавлення впливу зовнішнього попиту на рівні запасу ресурсів та забезпечення робастної стійкості замкнутої системи застосовано метод інваріантних еліпсоїдів, який зводить синтез оптимального регулятора до пошуку найменшого інваріантного еліпсоїда замкнутої системи. За допомогою лінійних матричних нерівностей задачу синтезу регулятора зведено до послідовності задач напіввизначеного програмування, які розв'язуються чисельно в реальному часі. Для зменшення ступеня консерватизму результатів керування застосовано дескрипторний підхід з використанням параметризованої функції Ляпунова. Сформульовано необхідні та достатні умови існування допустимого керування для розглянутої задачі. Задача оцінювання допустимої області в просторі керуючих впливів представлена у вигляді системи білінійних матричних нерівностей, для вирішення якої запропоновано ітераційний алгоритм. Побудовано математичну модель системи подачі та розподілу води як об'єкта автоматичного керування, яка відрізняється врахуванням нелінійних взаємозв'язків за умови існування квадратичних обмежень на їх значення. Розв'язано задачу автоматизації керування режимами роботи насосних станцій в системі централізованого водопостачання.
The dissertation for the degree of doctor of technical sciences, specialty 05.13.07 – automation of control processes. – The National Technical University "Kharkiv Polytechnic Institute", Kharkiv, 2016. The dissertation is devoted to the development of a concept and synthesis methods of automated systems of robust inventory control in supply networks with uncertainty of demand and time-delays on the basis of extension of the invariant ellipsoids method using the descriptor system approach and parameter-dependent Lyapunov function. A discrete mathematical model in state space of supply network is developed, which has parametric uncertainty of affine type. The control law is based on the periodic inspection of resources stock levels and constructed in the form of a linear dynamic feedback with respect to deviation between cash and safety stock levels of resources. In order to suppress the influence of the changes in external demand while ensuring robust stability of a closed system the invariant ellipsoids method is used, which reduces the synthesis of optimal controller to a problem of the search for the smallest invariant ellipsoid of the closed system. Using linear matrix inequalities the controller synthesis problem is reduced to a sequence of semidefinite programming problems, that are solved numerically in real time. A descriptor system approach with parameter-dependent Lyapunov function is used to reduce the degree of conservatism of control results. A necessary and sufficient conditions of the control existence for a constrained robust guaranteeing inventory control synthesis problem in supply networks are formulated. A problem of estimating the allowable region in the space of control actions is formulated in terms of solvability of bilinear matrix inequalities system, for solution of which an iterative algorithm is proposed. A mathematical model of the water distribution system as an automatic control object in the form of a set of linear subsystems with nonlinear relationships under condition of the existence of a quadratic constraints on their values is developed. A problem of pumping stations modes control automation in the centralized water supply system is solved.
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Conference papers on the topic "Invariant ellipsoid method"

1

Pesterev, Alexander V., and Lev B. Rapoport. "Ellipsoidal Approximations of Invariant Sets in Stabilization Problem for a Wheeled Robot Following a Curvilinear Path." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86199.

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A stabilization problem for a wheeled robot following a curvilinear target path is studied. In [1], a method for constructing invariant ellipsoids—quadratic approximations of the attraction domains for the target trajectory under a given control law—was developed. A basic result of that study is a theorem by means of which construction of the invariant ellipsoids reduces to solving a system of linear matrix inequalities (LMIs) and checking a scalar inequality. This paper is a sequel to work [1] and is devoted to practical implementation of the results obtained in that paper. It is discussed how to select the parameters in terms of which the theorem is formulated. An algorithm is developed that, for a given value of maximal deviation from the target trajectory, constructs an invariant ellipsoid of as large volume as possible.
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2

Polyakov, Andrey. "Invariant ellipsoid method for time-delayed predictor-based sliding mode control system." In 2010 11th International Workshop on Variable Structure Systems (VSS 2010). IEEE, 2010. http://dx.doi.org/10.1109/vss.2010.5544685.

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3

Gonzalez-Garcia, S., A. Polyakov, and A. Poznyak. "Output linear feedback for a class of nonlinear systems based on the invariant ellipsoid method." In 2008 5th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE). IEEE, 2008. http://dx.doi.org/10.1109/iceee.2008.4723431.

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4

Polyakov, Andrey, and Alex Poznyak. "Minimization of the unmatched disturbances in the sliding mode control systems via invariant ellipsoid method." In 2009 IEEE International Conference on Control Applications (CCA). IEEE, 2009. http://dx.doi.org/10.1109/cca.2009.5280842.

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5

Azhmyakov, Vadim. "On the geometric aspects of the invariant ellipsoid method: Application to the robust control design." In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC 2011). IEEE, 2011. http://dx.doi.org/10.1109/cdc.2011.6161180.

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6

Tan, Chun Kiat, and Jianliang Wang. "A novel PID controller gain tuning method for a quadrotor landing on a ship deck using the invariant ellipsoid technique." In 2014 14th International Conference on Control, Automation and Systems (ICCAS). IEEE, 2014. http://dx.doi.org/10.1109/iccas.2014.6987764.

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7

Gonzalez-Garcia, S., A. Polyakov, and A. Poznyak. "Linear feedback spacecraft stabilization using the method of invariant ellipsoids." In 2009 41st Southeastern Symposium on System Theory (SSST). IEEE, 2009. http://dx.doi.org/10.1109/ssst.2009.4806834.

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8

Khlebnikov, Mikhail. "An Approach to Tracking Problem for Linear Control System Via Invariant Ellipsoids Method." In 8th International Conference on Soft Computing, Artificial Intelligence and Applications. Aircc Publishing Corporation, 2019. http://dx.doi.org/10.5121/csit.2019.90714.

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Kalikhman, D. M., E. A. Deputatova, D. S. Gnusarev, V. M. Nikiforov, and I. Yu Bykanov. "Dynamic Output Regulator of the Angular Rate Sensor Built on the Invariant Ellipsoid Methods." In 2019 26th Saint Petersburg International Conference on Integrated Navigation Systems (ICINS). IEEE, 2019. http://dx.doi.org/10.23919/icins.2019.8769383.

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10

Davila, J., and A. Poznyak. "Sliding modes parameter adjustment in the presence of fast actuators using invariant ellipsoids method." In 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE 2009). IEEE, 2009. http://dx.doi.org/10.1109/iceee.2009.5393474.

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