Quantized feedback stabilization of impulsive switched linear systems based on event triggering

Abstract

This article studies the feedback stabilization problem of an impulsive switched linear system whose feedback loop is closed over a digital network. Particularly, the combined effects of mode switches, impulses, quantization, network delay and external disturbances on the stability of that system are investigated. By extending the previous delay-free and impulse-free methods of reachable-set approximation and propagation, some novel communication and control policies are designed to stabilize the concerned switched system with both network delay and impulses. In order to save the occupied network bandwidth, some event-triggered control policies are proposed. To handle the effects of the mode switches and the impulse, we design event-triggering conditions for both the case with no switch and no impulse on an inter-event interval and the case with one switch or one impulse on an inter-event interval. Note that the occurrence of a mode switch or an impulse leads to the switch of the event-triggering conditions. Under the event-triggered control policies, a stabilizing bit rate condition is derived. It is proven that even under impulses and network delay, the event-triggered control policies can stabilize the switched system at a lower bit rate than earlier works based on conventional time-triggered control policies.