Ultimate boundedness control for cyber-physical switched systems with try-once-discard protocol and uniform quantisation effects

This work addresses the ultimate boundedness control problem for a class of cyber-physical switched systems under average dwell time (ADT) switching, where both the Try-Once-Discard (TOD) protocol scheduling and the uniform quantisation effects happen on the communication network between the sensor node and the controller. Under the regulation of the TOD protocol, only one sensor node at each instant can access the network and transmit data. First, a nonlinear-observer-based switching controller is designed for the cyber-physical nonlinear switched system to ensure that the closed-loop system is ultimately bounded, and the controlled output is locally minimised in the presence of the TOD protocol and uniform quantisation effects. Then a TOD protocol-dependent convex Lyapunov function is first proposed, and the ultimate boundedness conditions of the closed-loop system in mean square are derived by the Lyapunov function. Furthermore, the controller gains are obtained by solving a convex optimisation problem. Finally, a numerical example is given to illustrate that the TOD protocol mechanism is used to eliminate network transmission congestion at the expense of some performance of the switched system by comparing the cases with and without the TOD protocol.