An Event-Triggered Approach to Sliding Mode Control of Markovian Jump Lur'e Systems Under Hidden Mode Detections

The asynchronous sliding mode control (SMC) problem is investigated for networked Markovian jump Lur'e systems, in which the information of system modes is unavailable to the sliding mode controller but could be estimated by a mode detector via a hidden Markov model (HMM). In order to mitigate the burden of data communication, an event-triggered protocol is proposed to determine whether the system state should be released to the controller at certain time-point according to a specific triggering condition. By constructing a novel common sliding surface, this paper designs an event-triggered asynchronous SMC law, which just depends on the hidden mode information. A combination of the stochastic Lur'e-type Lyapunov functional and the HMM approach is exploited to establish the sufficient conditions of the mean square stability with a prescribed performance and the reachability of a sliding region around the specified sliding surface. Moreover, the solving algorithm for the control gain matrices is given via a convex optimization problem. Finally, an example from the dc motor device system is provided.