Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

Zhao, Junjie; Shen, Hao; Li, Bo; Wang, Jing

doi:10.1007/s11071-013-0855-2

Cited by 40 publications

(18 citation statements)

References 27 publications

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“…It should be pointed out that finite-time stability does not imply Lyapunov stability, and Lyapunov stability does not contain finite-time stability since the transient behaviour of the system response may exceed the prescribed bound. Recently, some available results on finite-time control for Markovian switching system have been reported (He, 2010;Zhang, Liu, & Song, 2013;Zhao, Shen, Li, & Wang, 2013;Zuo, Liu, Wang, & Li, 2012).…”

Section: Introductionmentioning

confidence: 99%

Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

Gao

2015

International Journal of Systems Science

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This paper focuses on the problem of finite-time H ∞ control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity. By employing an appropriate Lyapunov function and some appropriate freeweighting matrices, a state feedback controller is designed to ensure H ∞ finite-time boundedness of the resulting closed-loop system that contains time-varying delay, admissible external disturbance, Itô-type stochastic disturbance and nonlinearity. All the proposed conditions are established in the form of linear matrix inequalities. Finally, an example is given to demonstrate the validity of the main results.

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Section: Introductionmentioning

confidence: 99%

Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

Gao

2015

International Journal of Systems Science

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“…Recently, some investigations are carried out on the MJSs with actuator saturation [37][38][39][40][41][42][43][44][45][46]. By applying appropriate Lyapunov functions, robust H ∞ controller for uncertain discrete-time MJSs is design to guarantee the stochastic stability of the corresponding closed-loop systems in [39].…”

Section: Markov Jump Systems (Mjss) Driven By Continuous-time Markov mentioning

confidence: 99%

“…Zhao et al investigated finite-time H ∞ control for a class of MjSs with actuator saturation and obtained a series of results [43][44][45]. Finite-time H ∞ control for a class of discrete-time Markov jump systems with actuator saturation was probed via dynamic anti-windup design in [46].…”

Section: Markov Jump Systems (Mjss) Driven By Continuous-time Markov mentioning

confidence: 99%

“…Compared with the existing results in [45,46,47,48], we investigate a class of Markovian jump continuous-time singular systems even with a standard Wiener process, not Markovian jump discrete-time systems. Compared with the existing results in [43,44,50], we introduce the general unknown transition rates for the Markov process, which is more general than the partly accessible transition rates. Here, the standard Wiener process, general unknown transition rates and singular system matrix are introduced to increase the difficulty of our research.…”

Section: Problem Formulationmentioning

confidence: 99%

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An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

Kao

Xie

Wang

2015

Journal of the Franklin Institute

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“…For instance, Zhang et al had investigated the robust finite‐time fuzzy H ∞ control problem. Zhao et al had proposed finite‐time H ∞ control for a class of Markovian jump delayed systems. In one study, Ma et al explored the finite‐time H ∞ control problem for a class of discrete‐time switched singular time‐delay systems with actuator saturation.…”

Section: Introductionmentioning

confidence: 99%

Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

Liu

Wang

2017

Intl J Robust & Nonlinear

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Summary This paper focuses on the problem of finite‐time H∞ control for one family of discrete‐time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete‐time close‐loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite‐time boundedness and sliding mode H∞ finite‐time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

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Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

Cited by 40 publications

References 27 publications

Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

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Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

Cited by 40 publications

References 27 publications

Finite-timeH∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

Finite-timeH∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

An anti-windup design to robust H∞ control for singular Markovian jump systems with actuator saturation and general unknown transition rates

Reliable sliding mode finite‐time control for discrete‐time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

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Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

Finite-timeH_∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity