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

In this work we address the observability and observer design problem for perturbed switched linear systems (SLS) subject to an unknown switching signal, 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 observers, 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.