On Necessary and Sufficient Conditions for Mode Observability of a Class of State Dependant Switched Systems

In this paper we give necessary and sufficient conditions for the mode observability of a class of switched systems, where the switching signal is state dependant. The switching conditions are given by an affine partition of the space Rⁿ. This is a partition where the hyperplane not necessarily crosses through zero. The mode observability conditions are obtained as a result of an algebraic analysis of the so called joint observability matrix. A characterization of the sets where these conditions are fulfilled is also obtained. This characterization is given by translations of the hyperplane generating the partition. The results are illustrated by some examples for specific cases including a mechanical switched system.