Observability and Observer Design for Continuous-Time Perturbed Switched Linear Systems under Unknown Switchings

time instant the evolving LS. Hybrid systems cap­ ture the continuous and discrete interaction that appears in complex systems ranging from biolog­ ical systems [14] to automotive systems [7]. For SLS, many contributions have been reported con­ cerning such basic system properties as stability, controllability, and observability. Since the conditions for the observability with unknown inputs of the individual LS have been already established [4], the main problem for the observability of SLS is then to infer, from the knowl­ edge of the continuous measurements, which LS is evolving. This is usually referred to as the distinguishability problem. This problem, together with the SLS observability, has been extensively studied in the literature for the case of known in­ puts [1,9,13,18,20]. However, the observability of continuous-time SLS subject to unknown dis­ turbances and unknown switching signals has re­ ceived less attention. In the context of unknown switching signals, the concept of observability of SLS becomes more Abstract. In th؛s work we address the observability and observer design problem for perturbed switched linear systems (SLS) subject to an unknown switching sig­ nal, where the continuous state and the evolving linear system (LS) are estimated from the continuous output in spite of the unknown disturbance. The proposed observer is composed of a collection of finite-time ob­ servers, one for each LS composing the SLS. Based on the observability results hereinafter derived and in the observer’s output estimation error, the evolving LS and its continuous state are inferred. Illustrative examples are presented in detail