Robust ∞ control for uncertain discrete-time-delay fuzzy systems via output feedback controllers

This paper investigates the problem of robust output feedback control for a class of uncertain discrete-time fuzzy systems with time delays. The state–space Takagi–Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust control for a class of uncertain nonlinear discrete delay systems.