Stabilization of a class of uncertain large-scale stochastic systems with time delays

Xie, Shaojun; Xie, Lihua

doi:10.1016/s0005-1098(99)00147-8

Cited by 133 publications

(67 citation statements)

References 10 publications

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“…On the other hand, the study of stochastic systems with time delays has mainly focused on robust stability analysis and stabilization in recent years, see for example, [17][18][19][20] and the references therein. In [17], several sufficient conditions ensuring exponential stability in mean-square sense for stochastic time-delay systems were given, while in [19] the robust stochastic stabilization problem was solved via a linear matrix inequality (LMI) approach. In [21], the problems of robust stabilization and robust H ∞ control for uncertain stochastic systems with state delay were studied, where sufficient conditions for the existence of state-feedback controllers guaranteeing stochastic stability and prescribed H ∞ performance of the closed-loop system were obtained in terms of an LMI.…”

Section: Introductionmentioning

confidence: 99%

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

Rui

Gao

Shi

2009

Intl J Robust & Nonlinear

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SUMMARYThis paper investigates the robust H ∞ control problem for stochastic systems with a delay in the state. Sufficient delaydependent conditions for the existence of state-feedback controllers are proposed to guarantee mean-square asymptotic stability as well as the prescribed H ∞ performance for the closed-loop systems. Moreover, the results are further extended to the stochastic time-delay systems with parameter uncertainties, which are assumed to be time-varying norm-bounded appearing in both the state and the input matrices. The appealing idea is to partition the delay, which differs greatly from the most existing results and reduces conservatism by thinning the delay partitioning. Numerical examples are provided to show the advantages of the proposed techniques.

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Section: Introductionmentioning

confidence: 99%

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

Rui

Gao

Shi

2009

Intl J Robust & Nonlinear

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“…Control problems for linear time delay systems in the form of (1) or in a variety of other forms have been a subject of extensive research (see, for example, [1,2,3,4,5,6,9,10,13,15,16,18,19,20,22,23,24,25,26] and the references there in).…”

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confidence: 99%

On Asymptotic Stabilizability of Discrete-time Linear Systems with Delayed Input

Lin¹

2007

Communications in Information and Systems

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Abstract. This paper examines the asymptotic stabilizability of discrete-time linear systems with delayed input. By explicit construction of stabilizing feedback laws, it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable (i.e., all the open loop poles are on or inside the unit circle.) It is further shown that such a system, when subject to actuator saturation, is semi-globally asymptotically stabilizable by linear state or output feedback.

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“…Then the time derivative of V(x(t)) along any trajectory of the closed-loop system (6) is given by where Taking into account the fact that the inequalities (5) hold, it follows immediately that Hence, V(x(t)) is a Lyapunov function for the closed-loop system (6). Therefore, the closed-loop system (6) is asymptotically stable and u i (t) = K i x i (t) is the guaranteed cost controller.…”

Section: Theorem 1 Consider the Large-scale Interconnected Systems (1mentioning

confidence: 99%

Guaranteed cost control for large‐scale systems under control gain perturbations

Mukaidani

Tanaka

Mizukami

2004

Electrical Engineering Japan

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SUMMARYThe guaranteed cost control problem of the decentralized robust control for large-scale systems with the normbounded time-varying parameter uncertainties and a given quadratic cost function is considered. Sufficient conditions for the existence of guaranteed cost controllers are given in terms of linear matrix inequality (LMI). It is shown that decentralized local state feedback controllers can be obtained by solving the LMI. The problem of guaranteed cost control for large-scale systems under the gain perturbations is also considered.

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Stabilization of a class of uncertain large-scale stochastic systems with time delays

Cited by 133 publications

References 10 publications

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

On Asymptotic Stabilizability of Discrete-time Linear Systems with Delayed Input

Guaranteed cost control for large‐scale systems under control gain perturbations

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Stabilization of a class of uncertain large-scale stochastic systems with time delays

Cited by 133 publications

References 10 publications

Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems

Delay‐dependent robust H∞ control for uncertain stochastic time‐delay systems

On Asymptotic Stabilizability of Discrete-time Linear Systems with Delayed Input

Guaranteed cost control for large‐scale systems under control gain perturbations

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Product

Resources

About

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems

Delay‐dependent robust H_∞ control for uncertain stochastic time‐delay systems