Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems

The paper is concerned with robust stabilization and H_∞ control of a class of uncertain discrete-time fuzzy systems. The class of uncertain systems is described by state space Takagi-Sugeno (TS) fuzzy models with linear nominal parts and norm-bounded parameter uncertainties in the state and output equations. First, a sufficient condition on robust stability of the fuzzy models is proposed. Then, H _∞-disturbance attenuation performance of the fuzzy models is analyzed. Some sufficient conditions are derived on robust H _∞-disturbance attenuation in which both robust stability and a prescribed H_∞ performance are required to be achieved, irrespective of the uncertainties. A numerical example shows the use of the results on the stabilization and H_∞-disturbance attenuation of a class of discrete-time nonlinear systems via fuzzy switch