Asynchronous dynamic event‐triggered reachable set control for semi‐Markov jump systems with hybrid attacks

Abstract This paper investigates reachable set problem for semi‐Markov jump systems (SMJSs) with bounded external disturbances and cyber attacks. The objective is to design a suitable controller, which can make all the states of the system from zero initial condition within a given reachable set. Firstly, a dynamic event‐triggered (DET) mechanism is introduced to make each subsystem rely only on its own state information during event detection. And DET mechanism also can decrease the wastage of sensing and networking resources. Secondly, an asynchronous approach is used to consider the unmatched behaviour between the system and controller modes. A suitable Lyapunov–Krasovskii functional (LKF) is introduced and applied to obtain an elliptic description of the system's reachable set. Then a sequence of feasible linear matrix inequalities (LMIs) are employed to obtain the controller gains. Finally, the effectiveness and practicability of the proposed method is verified by using a tunnel diode circuit model.