Non-fragile Robust H ∞ Fuzzy Controller Design for a Class of Nonlinear Descriptor Systems with Time-Varying Delays in States

Abstract

The controller fragility can cause the performance debasement of the closed-loop system due to small perturbations in the coefficients of the controller design, and is one of the most important factors to be considered during practical controller design. To take the controller fragility into consideration for a class of nonlinear time-delayed descriptor systems with norm-bounded time-varying uncertainties in the matrices of state, delayed state and control gain, we have proposed non-fragile robust H∞ fuzzy control design via state feedback controllers in this paper. The nonlinear descriptor system is approximated by Takagi-Sugeno (T-S) fuzzy model. In combination of parallel-distributed compensation (PDC) scheme, sufficient conditions are derived for the existence of non-fragile robust H∞ fuzzy controllers in terms of linear matrix inequalities (LMI). Finally, an example is given to demonstrate the use of the proposed controller design.