Delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time delays

doi:10.1016/j.fss.2010.09.015

Fuzzy Sets and Systems

Volume 164, Issue 1, 1 February 2011, Pages 66-81

https://doi.org/10.1016/j.fss.2010.09.015 Get rights and content

Abstract

This paper deals with the problem of delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time-varying delays. A delay-dependent stochastic stability condition for a fuzzy Markovian jump system with two levels of structure is obtained based on a new Lyapunov functional. The Lyapunov functional depends not only on the fuzzy basis functions but also on the system modes. Furthermore, a delay-dependent sufficient condition for the solvability of the robust stabilization problem is proposed in terms of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design method.

References (33)

Y.-Y. Cao et al.
Stochastic stabilizability and $H_{\infty}$ control for discrete-time jump linear systems with time delay
J. Franklin Inst.
(1999)
B. Chen et al.
Guaranteed cost control of T–S fuzzy systems with state and input delays
Fuzzy Sets and Systems
(2007)
W. Chen et al.
Delay-dependent stability and $H_{\infty}$ control of uncertain discrete-time Markovian jump systems with mode-dependent time delays
Syst. Control Lett.
(2004)
B.C. Ding et al.
Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi–Sugeno's form
Automatica
(2006)
J. Dong et al.
State feedback control of continuous-time T–S fuzzy systems via switched fuzzy controllers
Inf. Sci.
(2008)
T.M. Guerra et al.
LMI-based relaxed non-quadratic stabilization conditions for nonlinear systems in Takagi–Sugeno's form
Automatica
(2004)
C. Lin et al.
Delay-dependent LMI conditions for stability and stabilization of T–S fuzzy systems with bounded time delay
Fuzzy Sets and Systems
(2006)
C. Lin et al.
Less conservative stability conditions for fuzzy large-scale systems with time delays
Chaos Solitons Fractals
(2006)
S.K. Nguang et al.
Robust output feedback control design for fuzzy dynamic systems with quadratic stability constraints: an LMI approach
Inf. Sci.
(2006)
I.R. Petersen
A stabilization algorithm for a class of uncertain linear systems
Syst. Control Lett.
(1987)

A. Sala et al.

Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: application of Polya's theorem

Fuzzy Sets and Systems

(2007)

P. Shi et al.

Worst case control of uncertain jumping systems with multi-state and input delay information

Inf. Sci.

(2006)

K. Tanaka et al.

Stability analysis and design of fuzzy control systems

Fuzzy Sets and Systems

(1992)

H. Wu et al.

Robust fuzzy control for uncertain discrete-time nonlinear Markovian jump systems without mode observations

Inf. Sci.

(2007)

J. Xiong et al.

Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers

Automatica

(2006)

J. Xiong et al.

On robust stabilization of Markovian jump systems with uncertain switching probabilities

Automatica

(2005)

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Delay-dependent robust stabilization for uncertain discrete-time fuzzy Markovian jump systems with mode-dependent time delays

Abstract

J. Franklin Inst.

Fuzzy Sets and Systems

Syst. Control Lett.

Automatica

Inf. Sci.

Automatica

Fuzzy Sets and Systems

Chaos Solitons Fractals

Inf. Sci.

Syst. Control Lett.

Fuzzy Sets and Systems

Inf. Sci.

Fuzzy Sets and Systems

Inf. Sci.

Automatica

Automatica