A novel descriptor redundancy approach for non-quadratic robust H∞ control of T-S fuzzy nonlinear singularly perturbed systems

Abstract

A new design procedure for robust H∞ control for a class of T-S fuzzy singularly perturbed systems based on fuzzy Lyapunov functions and non-PDC control scheme is proposed in this paper. Using the proposed controller, the closed-loop TS fuzzy singularly perturbed system becomes asymptotically stable in the absence of disturbances and satisfies the H∞-norm condition in the presence of disturbances all positive values of the singular perturbation parameter within the given desired bound. The main drawback of a fuzzy Lyapunov-based approach is that one needs to find some upper or lower bounds for the derivatives of the grades of the membership functions, which is hard to find in practice. By using natural properties of a T-S model, a novel procedure is proposed to tackle this problem. Using the descriptor redundancy approach, the design conditions are derived in the form of some strict linear matrix inequalities (LMIs). Moreover, to cover a more general problem, it is assumed that there exist some uncertainties in the local system matrices of the T-S fuzzy singularly perturbed system. Two examples are presented to illustrate that the proposed design conditions are feasible for larger bounds on the singular perturbation parameter compared to those of previous techniques.