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

Abstract

International audienceThis 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

A polyhedral approach to the stability analysis and feedback stabilization of networked control systems

“…This Lemma is an extension to uncertain systems of a basic result developed for time-invariant systems [17]. Relations (12) and (13) …”

“…By treating the uncertain NCS delay as a time-varying parameter uncertainty, sufficient conditions, expressed as LMIs, for the existence of a static stabilizing state feedback controller appear in [8], [9], [10]. Also, switched system approaches have recently been developed in [11], [12].…”

Stability Criteria for Asynchronous Sampled-data Systems – A Fragmentation Approach

“…Note that the above problem is a semiinfinite dimensional convex feasibility problem which is difficult to solve due to the presence of exponential terms inÃ(T ) [Hetel et al, 2008, Fujioka, 2009a, Oishi and Fujioka, 2009]. As we shall see later, the obtained LMI conditions using statement (ii) are still semi-infinite but linear in the sampling-period and hence easy to check.…”

Comparison of stability characterisations for networked control systems

“…Based on this model, stability analysis conditions in terms of linear matrix inequalities (LMIs) will be derived, using both a common quadratic and a parameter dependent Lyapunov approach. Note that recently, in [12], a simplified event-based discretetime model has been proposed using the system's representation at both sampling and actuation times. The advantage of the model presented in this paper in comparison to this event-based model is that it generally leads to a discretetime representation of a smaller dimension.…”