Chapter 3 - On the Observability and Observer Design in Switched Linear Systems

Abstract

Switched linear systems (SLS) are dynamical systems formed by a collection of linear continuous state models switching among them according to a discrete signal. These systems have shown to be useful for representing complex behaviors of physical systems interacting with logical rules or controllers. The observability analysis in SLS has received a lot of attention in recent years. Several works can be found in the literature providing conditions for observability and observer algorithms, considering different assumptions on the inputs, initial states, and knowledge of the discrete information. In this chapter, a geometrical observability analysis is presented for the case in which no information about the switching rule is available, and there exist unknown inputs (disturbances). The analysis is performed for different cases, in which the property holds for all the state trajectories and for all applied inputs, or for “almost all” state trajectories and/or “almost all” inputs. Furthermore, a finite-time observer scheme is presented, which estimates both the discrete and the continuous states. Finally, it is shown how these results can be applied to the modulation/demodulation process in chaos-based secure communications.