Observability of Linear Hybrid Systems

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.

[1]  A. Haddad,et al.  On the Controllability and Observability of Hybrid Systems , 1988, 1988 American Control Conference.

[2]  R. Vidal,et al.  Observability and identifiability of jump linear systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  F. Szigeti,et al.  A differential-algebraic condition for controllability and observability of time varying linear systems , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[4]  J. Hespanha,et al.  Nonlinear observability and an invariance principle for switched systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[5]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[6]  Angelo Alessandri,et al.  Design of Luenberger Observers for a Class of Hybrid Linear Systems , 2001, HSCC.

[7]  Inseok Hwang,et al.  Observability criteria and estimator design for stochastic linear hybrid systems , 2003, 2003 European Control Conference (ECC).

[8]  J. Zakoian,et al.  Stationarity of Multivariate Markov-Switching ARMA Models , 2001 .

[9]  P. Ramadge.  Observability of discrete event systems , 1986, 1986 25th IEEE Conference on Decision and Control.

[10]  A. Willsky,et al.  Observability of discrete event dynamic systems , 1990 .

[11]  Alberto Bemporad,et al.  Observability and controllability of piecewise affine and hybrid systems , 2000, IEEE Trans. Autom. Control..

[12]  Thomas Kailath,et al.  Linear Systems , 1980 .

[13]  Alberto L. Sangiovanni-Vincentelli,et al.  Design of Observers for Hybrid Systems , 2002, HSCC.

[14]  Jitendra Tugnait,et al.  Adaptive estimation and identification for discrete systems with Markov jump parameters , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[15]  B. Moor,et al.  Subspace angles and distances between ARMA models , 2000 .

[16]  Shuzhi Sam Ge,et al.  Controllability and reachability criteria for switched linear systems , 2002, Autom..

[17]  Eduardo F. Costa,et al.  On the detectability and observability of discrete-time Markov jump linear systems , 2001, Syst. Control. Lett..

[18]  Eduardo F. Costa,et al.  On the observability and detectability of continuous-time Markov jump linear systems , 2001, ECC.