Sliding mode control of Markovian jump systems under multi-node round-robin protocol

In this paper, the sliding mode control problem is addressed for the networked Markovian jump system. In order to avoid data collision and congestion in transmission via the shared network, the scheduling of sensor signals towards the controller and controller signals towards the actuators is regulated by a novel round-robin protocol, the so-called multi-node round-robin protocol. This means that at each transmission instant, some consecutive actuator/sensor nodes (but not all) can access the transmission network, and the control/measurement information corresponding to other actuators/sensors is not updated. In order to deal with the incomplete transmission problem accounting for the considered protocol, a corresponding signal hold strategy is proposed to compensate for the unavailable signals. And then, a mode-token-dependent sliding mode controller is designed to ensure the reachability of the sliding surface, and sufficient conditions are presented to guarantee the stochastically ultimate bound of the resultant closed-loop system. Finally, a numerical example is adopted to illustrate the proposed method.