On the Observability of Continuous-Time Switched Linear Systems Under Partially Unknown Inputs

This technical note addresses the problem of observability of continuous-time Switched Linear Systems (SLS) subject to unknown disturbances, unknown switching signals and unconstrained nonzero dwell time. For this class of hybrid systems, a geometric characterization of the observability properties...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2012-03, Vol.57 (3), p.732-738
Main Authors: Gomez-Gutierrez, D., Ramirez-Trevino, A., Ruiz-Leon, J., Di Gennaro, S.
Format: Article
Language:English
Subjects:
Applied sciences
Automatic control
Bismuth
Computer science
control theory
systems
Control theory. Systems
Distinguishability
Disturbances
Dwell time
Estimation
Exact sciences and technology
Hybrid systems
Linear systems
Modelling and identification
Observability
Silicon
switched systems
Switches
Switching
System theory
Trajectory
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Summary:This technical note addresses the problem of observability of continuous-time Switched Linear Systems (SLS) subject to unknown disturbances, unknown switching signals and unconstrained nonzero dwell time. For this class of hybrid systems, a geometric characterization of the observability properties is presented. In particular, attention is focused on the estimation of the SLS state from the continuous measurements. Using the well known concept of (A, B)-invariant subspaces, three main problems are addressed and solved, namely the observability for every nonzero state trajectory, the observability for almost every control input, and the observability for almost every state trajectory. It is also shown that the approach herein presented subsumes some of the classical results on observability of SLS previously reported in the literature, and allows expressing them in a common framework.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2011.2166669