A bit rate condition for feedback stabilization of uncertain switched systems with external disturbances based on event triggering

Abstract

This paper studies the input-to-state stability of an uncertain switched linear system with external disturbances, whose feedback loop is closed over a digital communication network. In the network, only a finite bit rate can be provided to transmit the feedback signal and unknown network delay always exists. By using reachable set approximation and propagation methods, it can well handle with the effects of model uncertainty, external disturbances and network delay on the stability of the system. To save network resources, event-triggered sampling is taken here. Under the event-triggered sampling strategies, a new encoder is proposed, which consumes less feedback bits than the conventional time-triggered encoders. It is proven that even in the existence of model uncertainty, external disturbances and network delay, the proposed event-triggered sampling strategies require a lower feedback bit rate to stabilize the switched system than conventional periodic sampling methods.