Observability Linear Hybrid Systems

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 sucient conditions that the structural parameters of the model must satisfy in order for ltering 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 sucient to guarantee the uniqueness of the reconstruction of the state trajectory, even when the individual linear systems are unobservable.