State feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems with parameter uncertainty

Abstract

This study investigates the problem of state feedback robust stabilisation for discrete-time fuzzy singularly perturbed systems (SPSs) with parameter uncertainty. The considered system is approximated by Takagi–Sugeno fuzzy model. Based on a matrix spectral norm approach, new sufficient conditions, which ensure the existence of state feedback controller such that the resulting closed-loop system is asymptotically stable, are given. The gains of controllers are obtained by solving a set of ɛ-independent linear matrix inequalities (LMIs) such that, the ill-conditioned problems caused by ɛ can be easily avoided. In contrast to the existing results, the proposed method can be applied to both certain and uncertain SPSs with greater singular perturbation parameter ɛ. A numerical example is provided to illustrate the reduced conservatism of the authors’ results.