Date: 14 Mar 2003

Observability of Linear Hybrid Systems

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Abstract

We analyze the observability of the continuous and discrete states of continuous-time linear hybrid systems. For the class of jumplinear systems, we derive necessary and sufficient conditions that the structural parameters of the model must satisfy in order for filtering and smoothing algorithms to operate correctly. Our conditions are simple rank tests that exploit the geometry of the observability subspaces. For linear hybrid systems, we derive weaker rank conditions that are sufficient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.

Research supported by grants ONR N00014-00-1-0621, NSF STC “CENS” and ECS0200511, European Project RECSYS, MIUR National Project Identification and Adaptive Control of Industrial Systems and Italian Space Agency.