Analysis and control of LTI and switched systems in digital loops via an event-based modelling

This paper is dedicated to the modelling of LTI continuous time systems in digital control loops. We consider the digital control problem on non-uniform sampling periods. Moreover, we assume that time varying delays that may have a variation range larger than a sampling period affect the closed-loop. Our goal is to present a unique model that is able to include these problems simultaneously and that can be handled by classical control synthesis tools. We present a new event based discrete-time model (an exponential uncertain system with delay) and we show that the stabilizability of this system can be achieved by finding a control for a switched polytopic system with an additive norm bounded uncertainty. The methodology is extended to the case of switched system.