Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach

Gabriel, Gabriela W.; Gonçalves, Tiago R.; Geromel, J.C.

doi:10.1109/tac.2018.2797212

Cited by 37 publications

(20 citation statements)

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“…Um tratamento geral dos sistemas sujeitos a saltos Markovianosé dado em (Costa et al, 2013(Costa et al, , 2006. MJLSs híbridos são analisados em poucas referências na literatura, como em (Gabriel et al, 2018), no contexto de sistemas amostrados. No entanto, no melhor conhecimento dos au-tores, não há, na literatura atual, trabalhos que analisem a estrutura proposta aqui.…”

Section: Trabalhos Relacionadosunclassified

Análise e Controle de Sistemas Lineares Híbridos Sujeitos a Saltos Markovianos

Araujo

Fioravanti

Gonçalves

et al. 2019

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

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In this work, we present a hybrid Markov jump linear system model. We devise sufficient conditions for stability and performance, together with mode-dependent state-feedback control design conditions for such systems. Numerical experiments validate the developed theory. Resumo: Neste trabalho, apresentamos um modelo de sistema linear híbrido sujeito a saltos Markovianos. Desenvolvemos condições suficientes de estabilidade e de desempenho, assim como condições de projeto de controladores dependentes do modo via realimentação de estado para tais sistemas. Simulações numéricas validam a teoria desenvolvida.

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Section: Trabalhos Relacionadosunclassified

Análise e Controle de Sistemas Lineares Híbridos Sujeitos a Saltos Markovianos

Araujo

Fioravanti

Gonçalves

et al. 2019

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

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“…See also Todorov and Fragoso (2011) where useful results on stability radii of MJLS are provided. A hybrid approach together with MJLS has been used in Gabriel, Geromel, and Grigoriadis (2017) and Gabriel, Gonçalves, and Geromel (2018), in which the design conditions for stability and optimal H 2 and H ∞ sampled-data state feedback control are necessary and sufficient. In the mentioned references, the following control structure has been adopted…”

Section: Introductionmentioning

confidence: 99%

“…This kind of structure is necessary, for example, when the controller and the sensors are physically distant to each other. Since the Markov jump parameter in the control signal is not affected by the sampling operation, it is necessary to include new mathematical devices in the associated hybrid system, when comparing to the one given in Gabriel et al (2018). Unfortunately, as it will be clear afterward, the design problem that considers the control law (1) is much more difficult to solve than the second one whose optimal solution is available in the literature, see Gabriel et al (2018).…”

Section: Introductionmentioning

confidence: 99%

“…Since the Markov jump parameter in the control signal is not affected by the sampling operation, it is necessary to include new mathematical devices in the associated hybrid system, when comparing to the one given in Gabriel et al (2018). Unfortunately, as it will be clear afterward, the design problem that considers the control law (1) is much more difficult to solve than the second one whose optimal solution is available in the literature, see Gabriel et al (2018). Hence, the novelty of this paper is to address the previously mentioned control design problem where the gain matrix changes according to the actual state of the Markov chain.…”

Section: Introductionmentioning

confidence: 99%

“…In this case, to be able to formulate a convex programming problem, some algebraic issues must be faced leading to a result with a certain degree of conservatism. Moreover, considering the DLMI-based procedure proposed in Gabriel et al (2018), the control design conditions are easily solved by any LMI solver. Two examples borrowed from the literature illustrate the theoretical results.…”

Section: Introductionmentioning

confidence: 99%

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Robust partial sampled-data state feedback control of Markov jump linear systems

Cunha

Gabriel

Geromel

2019

International Journal of Systems Science

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This paper proposes new conditions for the design of a robust partial sampled-data state feedback control law for Markov jump linear systems (MJLS). Although, as usual, the control structure depends on the Markov mode, only the state variable is sampled in order to cope with a specific network control structure. For analysis, an equivalent hybrid system is proposed and a two-point boundary value problem (TPBVP) that ensures minimum H ∞ or H 2 cost is defined. For control synthesis, it is rewritten as a convex set of sufficient conditions leading to minimum guaranteed cost of the mentioned performance classes. The optimality conditions are expressed through differential linear matrix inequalities (DLMIs), a useful mathematical device that can be handled by means of any available LMI solver. Examples are included for illustration.

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Aperiodic sampled‐data controller design for stochastic Markovian jump systems and its application

Yang

Wang

Huang

et al. 2021

Intl J Robust & Nonlinear

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In this paper, aperiodic sampled‐data controller design problem is solved for stochastic Markovian jump systems (SMJSs). By introducing mode‐dependent one‐sided loop‐based Lyapunov functional and mode‐dependent two‐sided loop‐based Lyapunov functional and using Itô formula, two different stochastic stability conditions for SMJSs under aperiodic sampled‐data control are presented, respectively. Based on these two stability conditions, corresponding mode‐dependent aperiodic sampled‐data controller is designed for SMJSs. Finally, practical aircraft model are applied to illustrate the effectiveness of the method. It is also shown that mode‐dependent two‐sided loop‐based Lyapunov functional can obtain a larger upper bound of the sampling interval than mode‐dependent one‐sided loop‐based Lyapunov functional.

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Optimal and Robust Sampled-Data Control of Markov Jump Linear Systems: A Differential LMI Approach

Cited by 37 publications

References 20 publications

Análise e Controle de Sistemas Lineares Híbridos Sujeitos a Saltos Markovianos

Análise e Controle de Sistemas Lineares Híbridos Sujeitos a Saltos Markovianos

Robust partial sampled-data state feedback control of Markov jump linear systems

Aperiodic sampled‐data controller design for stochastic Markovian jump systems and its application

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