Chapter

Hybrid Systems: Computation and Control

Volume 2623 of the series Lecture Notes in Computer Science pp 526-539

Date:

Observability of Linear Hybrid Systems

  • René VidalAffiliated withDepartment of EECS, University of California
  • , Alessandro ChiusoAffiliated withDipartimento di Ingegneria dell’Informazione, Università di Padova
  • , Stefano SoattoAffiliated withDepartment of CS, University of California
  • , Shankar SastryAffiliated withDepartment of EECS, University of California

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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.