Dissipativity-Based Asynchronous Control for 2-D Markov Jump Systems in Continuous-Time Domain

In Markov jump systems (MJSs), it is really difficult for the controller to perfectly follow the plant’s mode transitions due to a number of practical factors. Therefore, this article considers to develop an asynchronous controller for a class of two-dimensional continuous-time MJSs. The relation of the plant’s mode and the controller’s mode is modeled by the hidden Markov model, i.e., the plant’s mode influences the controller’s transitions in a conditional probabilistic style. By defining a vector Lyapunov function, a sufficient condition for mean-square exponential stability and ( $\mathcal U$ , $\mathcal R$ , $\mathcal S$ )- $\varepsilon $ dissipativity is derived, whose feasible solutions give birth to a desired asynchronous controller. Finally, the influence of conditional probabilities on dissipativity performance is further studied through simulations.