Observability Reduction of Piecewise-affine Hybrid Systems

We present necessary conditions for observability of piecewise-affine hybrid systems. We also propose an ob- servability reduction algorithm for transforming a piecewise- affine hybrid system to a hybrid system of possibly smaller dimension which satisfies the formulated necessary condition for observability. I. INTRODUCTION In this paper we present necessary conditions for observ- ability of piecewise-affine systems (abbreviated as PAHSs) and a dimensionality reduction procedure, based on this necessary condition. A PAHS is a hybrid systems, continuous dynamics of which is determined by affine control systems, the reset maps are affine and the guards are polyhedral sets. The definition of PAHS adopted in this paper is essentialy the same as in (7), except that we allow the continuous state-space to be also a polyhedron as opposed to a polytope. Contribution of the paper The contribution of the paper can be summarized as follows.