Input-to-State Stability of the Nonlinear Fuzzy Systems via Small-Gain Theorem and Decentralized Sliding-Mode Control

This article presents the input-to-state stability (ISS) and decentralized sliding-mode control of polynomial fuzzy interconnected systems by using the small-gain theorem. The contribution of this article is threefold. First, based on the boundedness of the solution of fuzzy interconnected subsystems, the sufficient conditions for the boundedness fuzzy interconnected system are provided. Second, the ISS small-gain theorem is extended to the polynomial fuzzy interconnected system for the number of membership functions being the same and different, and the trajectory-based ISS small-gain theorem is proposed. Third, the sliding surface based on state feedback is designed, and the stability of sliding-mode motion is analyzed for the fuzzy interconnected system. Finally, the effectiveness and superiority of the proposed method are illustrated by using a numerical example, a spring-connected double inverted pendulum system, and comparison with the existing results.