H∞ Fuzzy Output Feedback Control Design for Nonlinear Systems: An LMI Approach

This paper addresses the problem of stabilizing a class of nonlinear systems by using an H8 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 H8 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 H8 fuzzy output feedback controller is given. In contrast to the existing results, the premise variables of the H8 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.