Dissipativity-Based Composite Antidisturbance Control for T–S Fuzzy Switched Stochastic Nonlinear Systems Subjected to Multisource Disturbances

Abstract

In this article, a dissipativity-based composite antidisturbance control structure is constructed for Takagi–Sugeno (T–S) fuzzy switched stochastic nonlinear systems subjected to multisource disturbances. The inherent uncertain nonlinear and hybrid characteristics of the concerned system make it difficult to design a stable antidisturbance controller. To properly accommodate the characteristics of T–S fuzzy multisource disturbances and system models, a novel fuzzy switched disturbance observer is put forward to estimate the disturbances generated by a switched exogenous system. Then, a fuzzy composite antidisturbance control law is synthesized by fusing the estimation of the multisource disturbances and the state-feedback control scheme. By using the average dwell time technique and piecewise Lyapunov functions, it is proved that the resultant closed-loop system are stochastically stable and strictly $({{\mathscr Z},{\mathscr Y},{\mathscr X}})-\varepsilon -$ dissipative. The sufficient conditions for the existence of the fuzzy switched disturbance observer and state-feedback controller are established in terms of linear matrix inequalities, and the control and observation gains can be solved directly. Finally, a numerical example is presented to illustrate the effectiveness and favor performance of the proposed control algorithm.