About the observability of piecewise dynamical systems

Abstract

In this paper, we give some sufficient geometrical conditions to analyse the observability of a class of hybrid systems: piecewise-smooth dynamical systems. For the subclass of piecewise linear systems, the analysis of the observability is refined. Indeed, thanks to the algebraic structure of this subclass, we improve one of these sufficient conditions by using the rank of a matrix associated to a piecewise linear system. This matrix takes into account all the observability matrices of the subsystems as well as the switch linear function. Throughout this paper we give examples to highlight our method.