Mixed H2/H∞ fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach

This study introduces a mixed 2 fuzzy output feedback control design method for nonlinear systems with guaranteed control performance. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a fuzzy observer-based mixed 2 controller is developed to achieve the suboptimal 2 control performance with a desired disturbance rejection constraint. A robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure. By the proposed decoupling technique and two-stage procedure, the outcome of the fuzzy observer-based mixed 2 control problem is parameterized in terms of two eigenvalue problems (EVP’s)—one for observer and the other for controller. The EVP’s can be solved very efficiently using the linear matrix inequality (LMI) optimization techniques. A simulation example is given to illustrate the design procedures and performances of the proposed method.