Asynchronous Event-Triggered Sliding Mode Control for Semi-Markov Jump Systems within a Finite-Time Interval

In this paper, the finite-time sliding mode control issue is studied for a series of semi-Markov jump systems subject to actuator faults, where an asynchronous control method is adopted to overcome the non-synchronous phenomenon between the system mode and controller mode. Additionally, the event-triggered protocol, which determines whether the transmission of data should be performed according to the threshold condition, is introduced to alleviate the burden of data transmission in the communication channel. This paper aims to devise an asynchronous event-triggered sliding mode control law so as to guarantee the trajectories of the resulting closed-loop system can be forced onto the predefined sliding surface in a finite-time interval. Thence, by means of the mode-dependent Lyapunov functions and the finite-time theory, sufficient conditions are derived to assure that the closed-loop system is mean-square finite-time bounded in both reaching and sliding motion phases. Eventually, a numerical example and a tunnel diode circuit model are presented to illustrate the availability and practicability of the proposed approach.