H∞ fuzzy output feedback control design for nonlinear systems: an LMI approach

Addresses the problem of stabilizing a class of nonlinear systems by using an H_∞ fuzzy output feedback controller. First, a class of nonlinear systems is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, based on a well-known Lyapunov functional approach, we develop a technique for designing an H_∞ fuzzy output feedback control law which guarantees the L₂ gain from an exogenous input to a regulated output is less or equal to a prescribed value. A design algorithm for constructing an H_∞ fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H_∞ fuzzy output feedback controller are not necessarily to be the same as the premise variables of the TS fuzzy model of the plant. A numerical simulation example is presented to illustrate the theory development.