Output feedback H∞H∞ control for uncertain discrete-time hyperbolic fuzzy systems

The paper deals with the problem of output feedback H∞H∞ control for a class of uncertain discrete-time fuzzy systems with hyperbolic models. The hyperbolic model can be obtained from a set of linguistic rules. The uncertainties in the systems under consideration are assumed to be of linear fractional form, which includes the norm-bounded uncertainty as a special case and can describe a class of rational nonlinearities. A sufficient condition for robust stability with H∞H∞ norm bound of the hyperbolic system is obtained in terms of a linear matrix inequality (LMI). Moreover, an output feedback controller can be constructed to guarantee the closed-loop system being robustly stable with H∞H∞ norm bound. Finally, a numerical example is given to demonstrate the applicability of the proposed approach.