Finite-Time Stabilization for Discontinuous Interconnected Delayed Systems via Interval Type-2 T–S Fuzzy Model Approach

Abstract

This paper investigates the finite-time stabilization for a class of interconnected systems with nonlinear discontinuous interconnections in which the time-varying delay are considered. By utilizing the universal approximation ability of the fuzzy model, a unified interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy-model-based interconnected delayed system is provided. Then, in order to solve the existence of solution for the concerned system with discontinuous right-hand side, the Filippov solutions are defined based on differential inclusion theory and set-valued analysis. Furthermore, by the IT2 T–S fuzzy model approach, a delayed state feedback controller equipped with discontinuous term and time-varying delays term is proposed. According to the classical finite time stability theory and generalized Lyapunov approach, finite-time stabilization for the discontinuous interconnected delayed system is achieved, and the estimate of settling time is given. Moreover, when the detailed information of time-varying delays is unknown, the finite-time stabilization is also realized via another improved controller, which only depends upon the upper bound of time-varying delays. Finally, the proposed methodologies are illustrated by a numerical example.