Robust H∞ fuzzy control via dynamic output feedback for discrete-time systems

A fuzzy control system consisting of a discrete-time T-S fuzzy model with Frobenius norm-bounded uncertainties and a fixed order dynamic output feedback controller is proposed in this paper. By using a quadratic Lyapunov function., both globally exponential stability and robust H_∞ performance are demonstrated. Two sufficient conditions are stated. One is expressed in terms of nonlinear matrix inequalities, the other is stated in terms of linear matrix inequalities. The former is only existential while the latter is solvable in terms of linear matrix inequalities searching for the existence of a robust H_∞ dynamic output feedback fuzzy controller. It is shown that the control laws can be obtained by LMI techniques after a suitable transformation that transforms the existential nonlinear matrix inequalities condition into a solvable LMIs condition