An LMI approach for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml45" display="inline" overflow="scroll" altimg="si4.gif"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml46" display="inline" overflow="scroll" altimg="si2.gif"><mml:msub><mml:mrow><mml:mi mathvariant="script">H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:

Morais, Cecília F.; Palma, Jonathan M.; Peres, Pedro L. D.; Oliveira, Ricardo C. L. F.

doi:10.1016/j.automatica.2018.06.014

Cited by 25 publications

(11 citation statements)

References 30 publications

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“…RP 1i E T and indicates irrelevant matrices. Then, applying (33), (36) and (37) to conditions (15) and (16), respectively, we have (20) and…”

Section: Resultsmentioning

confidence: 99%

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Zhang

2020

IEEE Access

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This paper considers the reduced-order H ∞ filtering problem for singular Markovian jump systems (SMJSs) with incomplete transition rates (ITRs) by using augmented system method. The considered conditions in this paper are necessary and sufficient (NS), whereas the existing conditions are mainly sufficient. To be concrete, by extracting system matrices in the considered system from augmented system, NS condition for the existence of the full-order H ∞ filtering is provided in terms of linear matrix inequalities (LMIs). However, it is hard to extend the condition to the existence of the reduced-order H ∞ filtering. Thus, by fixing augmented system matrices, NS condition for the existence of the reduced-order one is presented to guarantee the desired filtering error system to be stochastically admissible with H ∞ performance level. Furthermore, there are neither complicated matrix transformation nor equality/rank constraints in this paper. One numerical and one practical examples are illustrated to demonstrate the effectiveness of the achieved results. INDEX TERMS Singular Markovian jump system, incomplete transition rates, sufficient and necessary conditions, reduced-order filtering.

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“…RP 1i E T and indicates irrelevant matrices. Then, applying (33), (36) and (37) to conditions (15) and (16), respectively, we have (20) and…”

Section: Resultsmentioning

confidence: 99%

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Zhang

2020

IEEE Access

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“…Nevertheless, the parameters of RSNSs are invariant in the aforementioned researches. To all appearances, such systems are defective due to the random switch of the system parameters in some imperfect environments [3–8]. In this regard, can we find a model to describe the stochastic switch of system parameters?…”

Section: Introductionmentioning

confidence: 99%

Generalised dissipative asynchronous output feedback control for Markov jump repeated scalar non‐linear systems with time‐varying delay

Wang

Huo

Xia

et al. 2019

IET Control Theory & Applications

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“…Muitos pesquisadores têm abordado questões relevantes sobre tais sistemas, como estabilidade, filtragem, síntese de controle e controlé otimo, etc. ( (Shi and Li, 2015), (Shi et al, 1999), (Costa et al, 1999), (Vargas et al, 2013), (Geromel et al, 2009), (Morais et al, 2018), (Costa and Tuesta, 2003), (Oliveira et al, 2014)).…”

Section: Introductionunclassified

Controle robusto de horizonte finito em sistemas lineares com parâmetros variantes no tempo e saltos Markovianos

Lopes

Mendes

Vargas

et al. 2019

Anais Do 14º Simpósio Brasileiro De Automação Inteligente

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This paper presents a strategy to calculate a suboptimal solution to the finite-time linear-quadratic control problem of Markov jump linear systems. When the mode is fixed, the system has parameter-varying matrices that take values in a polutopic set. An upper bound for the cost function is obtained and, as a consequence, the feedback gains are calculated by solving an optimization problem written in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Resumo: Este trabalho apresenta uma estratégia para calcular uma solução subótima para o problema de controle linear quadrático de tempo finito de sistemas lineares com saltos Markovianos. Quando os modos são fixados, o sistema tem matrizes com parâmetros variantes, os quais tomam valores em um conjunto politópico. Um limitante superior para a função custoé obtido, como consequência, os ganhos de realimentação são calculados resolvendo um problema de otimização escrito em termos de desigualdades matriciais lineares. Um exemplo numéricoé dado para ilustrar a eficácia do método proposto.

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An LMI approach for H2 and H∞

Cited by 25 publications

References 30 publications

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Reduced-Order Filtering for Singular Markovian Jump Systems With Incomplete Transition Rates

Generalised dissipative asynchronous output feedback control for Markov jump repeated scalar non‐linear systems with time‐varying delay

Controle robusto de horizonte finito em sistemas lineares com parâmetros variantes no tempo e saltos Markovianos

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