• Journal of the Korean Institute of Intelligent Systems
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• v.19 no.6
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• pp.779-786
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• 2009

This paper deals with $H_{\infty}$ fuzzy control problem of discrete-time nonlinear Markovian jump systems with time delay. The Takgi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the Markovian jump fuzzy system with time delay. Stochastic Lyapunov function is dependent on the operation modes of the system. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller are given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficient of the proposed design methods.

• Journal of the Korean Institute of Intelligent Systems
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• v.22 no.1
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• pp.28-35
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• 2012

This paper presents the method for $H_{\infty}$ fuzzy controller design of discrete-time fuzzy Markovian jump systems with state and input time delays. The Takagi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the fuzzy Markovian jump systems with state and input time delays. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller is given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficiency of the proposed design method.