Event-based reachable set synthesis for delayed nonlinear semi-Markov systems

In this study, the issue of the reachable set (RS) synthesis for delayed nonlinear semi-Markov jump systems (s-MJSs) is addressed. An asynchronous controller whose controller mode is different from the system mode is designed. Non-fragile issues are considered in the design of the controller to improve the performance of the controller. Meanwhile, in order to economize on communication resources, the introduction of an event-triggered mechanism is considered in this work. A sufficient condition for the linear matrix inequalities (LMIs) form is obtained by utilizing the theory of Lyapunov functionals and the free-weighting matrix method, which ensures that the RS of the system is constrained by a compact ellipsoid. The controller gains of the system are then obtained by matrix decoupling. Ultimately, a numerical simulation and a practical model are provided to highlight the usability and practicality of the method.