Finite-Region Dissipative Control for 2-D Fuzzy Jump Systems Under Hidden Mode Detection

In this work, we consider the problem of finite-region asynchronous dissipative control and pay more attention to the transient behavior of a class of two-dimensional fuzzy Markov jump systems (MJSs). First, the considered plant is modeled based on a well-known Fornasini–Marchesini equation. The asynchronization phenomenon between the system modes and controller modes is characterized by a hidden Markov model. Then, by a fuzzy-basis-dependent and mode-dependent Lyapunov function, sufficient conditions are established, which can make the overall closed-loop fuzzy dynamic MJSs be finite-region bounded with a strictly $(T, S, R)$ - $\theta $ -dissipative performance. Finally, a numerical example concerning the Darboux equation is employed to validate the effectiveness and performance of the presented control scheme.