Robust stabilization for delayed discrete-time fuzzy systems via basis-dependent Lyapunov–Krasovskii function

Abstract

This paper deals with the robust control problem for a class of uncertain discrete-time fuzzy systems with time delay. The uncertainty is assumed to be of structured linear fractional form, which includes the norm-bounded uncertainty as a special case and can describe a class of rational nonlinearities. By using basis-dependent Lyapunov–Krasovskii function, a robust control design approach is developed. The control design approach is facilitated by introducing some additional instrumental matrix variables. These additional matrix variables decouple the Lyapunov–Krasovskii and the system matrices, which make the control design feasible. The proposed approach leads to some sufficient results in the form of strict linear matrix inequalities (LMIs). The development represents an important step towards reducing the conservatism of previous design methods, and the results also generalize earlier works for a more general parametric uncertainty structure. Numerical examples are also given to demonstrate the applicability of the proposed approach.