Stability Analysis and Dynamic Output Feedback Control for Nonlinear T-S Fuzzy System with Multiple Subsystems and Normalized Membership Functions

This paper addresses the stability analysis and dynamic output-feedback control problems for a class of nonlinear Takagi-Sugeno (T-S) fuzzy systems with multiple subsystems and normalized membership functions. First, the switching control law of the membership function is proposed based on the membership function for the nonlinear T-S fuzzy subsystems. Secondly, the relaxation parameter is introduced into this switching control law to guarantee a minimal dwell time between two consecutive switching. Then, based on the proposed switching control law of the membership function and relaxation parameter, the dynamic output feedback controller with the estimate algorithm is designed to estimate the attraction domain. By introducing the new switched Lyapunov-Krasovskii functional, it can be seen that the solutions of the resultant closed-loop system converge to an adjustable bounded region. Compared with the previous works, the developed controller in this paper is flexible and smooth, which only uses the system output. And the results are further extended to the mobile robot case and the chemical process case. Finally, two simulation examples are performed to show the effectiveness of the theoretical results.