H ∞ Fuzzy Control for Nonlinear Singular Markovian Jump Systems with Time Delay

Abstract EN

This paper investigates the problem of H ∞ fuzzy control for a class of nonlinear singular Markovian jump systems with time delay.

This class of systems underconsideration is described by Takagi-Sugeno (T-S) fuzzy models.

Firstly, sufficientcondition of the stochastic stabilization by the method of the augmented matrixis obtained by the state feedback.

And a designed algorithm for the state feedbackcontroller is provided to guarantee that the closed-loop system not only is regular,impulse-free, and stochastically stable but also satisfies a prescribed H ∞ performance for all delays not larger than a given upper bound in terms of linear matrixinequalities.

Then H ∞ fuzzy control for this kind of systems is also discussed by the static output feedback.

Finally, numerical examples are given to illustrate thevalidity of the developed methodology.