Bounded real lemma and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg"><mml:msub><mml:mi>H</mml:mi><mml:mi>∞</mml:mi></mml:msub></mml:math>control for singular Markovian jump systems with mode-dependent derivative-term coefficient

Tian, Yufeng; Wang, Zhanshan

doi:10.1016/j.jfranklin.2020.11.004

Cited by 2 publications

(7 citation statements)

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“…Proof. First, we will show the stochastic admissibility for system (11) with ω(t) � 0. It can be obtained from ( 18) and ( 19) that…”

Section: Resultsmentioning

confidence: 99%

“…Due to a stochastic variable of Bernoulli distribution, filtering error system ( 11) is established as a stochastic T-S fuzzy singular system. In this condition, the definition of admissibility in [19] does not work for the stochastic T-S fuzzy singular system in (11) anymore. Motivated by the stochastic admissibility defined in [36] of Complexity the discrete time case, we can generalize the definition of admissibility in [19] naturally and have the following definition of stochastic admissibility for system (11).…”

Section: Problem Formulationmentioning

confidence: 99%

“…(1) System ( 11) is said to be stochastically regular if det(E sE 11) is said to be stochastically impulse-free if deg(det (11) with ω(t) � 0 is said to be stochastically stable if there exists a scalar M > 0 such that…”

Section: Problem Formulationmentioning

confidence: 99%

“…where η(s, ϕ ∧ (t)) represents the system solution ( 4) System (11) with ω(t) � 0 is said to be stochastically admissible if it is stochastically regular, impulse-free, and stable Definition 2 (see [33]). Give real symmetric matrices Q and R and matrix S. For a scalar c > 0, if the equation…”

Section: Problem Formulationmentioning

confidence: 99%

“…Up to now, various results for studying singular time-delay systems have been published. Reachable set estimation for continuous-time singular delay systems [3][4][5], sliding mode control for discretetime singular delay systems [6][7][8], and H ∞ control for singular time-delay systems with Markovian jump parameters [9][10][11] are just a few examples of so many research works.…”

Section: Introductionmentioning

confidence: 99%

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Dissipative Filter Design for Nonlinear Time-Varying-Delay Singular Systems against Deception Attacks

2021

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This paper applies a T-S fuzzy model to depict a class of nonlinear time-varying-delay singular systems and investigates the dissipative filtering problem for these systems under deception attacks. The measurement output is assumed to encounter random deception attacks during signal transmission, and a Bernoulli distribution is used to describe this random phenomena. In this case, the filtering error system modeled by a stochastic singular T-S fuzzy system is established and stochastic admissibility for this kind of system is defined firstly. Then, by combining some integral inequalities and using the Lyapunov–Krasovskii functional approach, sufficient delay-dependent conditions are presented based on linear matrix inequality techniques, where the system of filtering error can be stochastically admissible and strictly ℚ , S , ℝ -dissipative against randomly occurring deception attacks. Moreover, parameters of the desired filter can be obtained via the solutions of the established conditions. The validity of our work is illustrated through a mostly used example of the nonlinear system.

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“…Proof. First, we will show the stochastic admissibility for system (11) with ω(t) � 0. It can be obtained from ( 18) and ( 19) that…”

Section: Resultsmentioning

confidence: 99%