H∞ and mixed H2/H∞ control of discrete-time T–S fuzzy systems with local nonlinear models

This paper addresses the H∞ and mixed H2/H∞ control synthesis problems of nonlinear discrete-time systems, which are represented by a new type of T–S fuzzy models. The fuzzy systems consist of local nonlinear models and are with fewer fuzzy rules than the conventional T–S fuzzy systems with local linear models. A fuzzy control scheme with local nonlinear feedbacks is proposed and H∞ and mixed H2/H∞ control synthesis conditions are 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 be used to design fuzzy controllers based on fewer control rules as well as are 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.