Design of fuzzy TS controller for simultaneous stabilization of nonlinear systems

In this paper, the problem of simultaneous stabilization of a collection of nonlinear systems is proposed by using the Takagi-Sugeno (TS) fuzzy modeling and synthesis approach. In practice, due to the uncertainty in the system model, failure modes, or different operating points, we often encounter the problem of simultaneous stabilization. The TS fuzzy model has been considered for the controller design of complex nonlinear systems as it provides a simple and effective concept. This problem refers to the stabilization of some nonlinear systems by utilizing a single nonlinear controller. Both state feedback and output feedback controllers are designed based on the PDC concept and by solving some linear matrix inequalities (LMIs). Moreover, to reduce the conservatisms related to using the common Lyapunov function and restrictive equality conditions in the design method, Finsler’s lemma has been employed. Finally, three numerical examples are provided to show that the proposed controllers stabilize well-considered nonlinear systems.