H∞ control of discrete-time T-S fuzzy systems with local nonlinear models

Abstract This paper addresses the H∞ control synthesis problem of nonlinear discrete-time systems, which are represented by a new type of T-S fuzzy systems. The fuzzy systems consist of local nonlinear models and with fewer fuzzy rules than the conventional T-S fuzzy systems with local linear models. A fuzzy control scheme with a nonlinear feedback control law in each control rule is proposed and an H∞ control synthesis condition is given in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing conditions for designing fuzzy controllers, the new ones can design fuzzy controllers based on fewer control rules as well as with less computational burden. In particular, the new methods can also give less conservative results. A numerical example is given to illustrate the effectiveness of the proposed methods.