Finite-Time Composite Antidisturbance Control for T–S Fuzzy Nonhomogeneous Markovian Jump Systems via Asynchronous Disturbance Observer

This article studies the finite-time composite antidisturbance control problem for nonhomogeneous Markovian jump systems (MJSs) subject to multiple disturbances via the Takagi–Sugeno (T–S) fuzzy control scheme. The designed two-gains disturbance observer (DO) and the considered MJSs are supposed to switch the different Markovian chains, which are depicted by a hidden Markovian model. Herein, an asynchronous DO design is explored for the first time, providing new insight into the construction of asynchronous DO. First, the $H_\infty /L_{2}-L_\infty$ finite-time boundedness of the augmented system is guaranteed. Second, based on the Finsler lemma, the linearization issue in calculating observer/controller gain is addressed. Finally, two illustrations are presented to verify the effectiveness of the proposed method.