Observability of linear hybrid systems

  • Authors:

  • René Vidal;Alessandro Chiuso;Stefano Soatto;Shankar Sastry

  • Affiliations:

  • Department of EECS, University of California, Berkeley, CA;Dipartimento di Ingegneria dell’Informazione, Università di Padova, Italy;Department of CS, University of California, Los Angeles, CA;Department of EECS, University of California, Berkeley, CA

  • Venue:
  • HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
  • Year:
  • 2003

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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 jump-linear 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.