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

• 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
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2011.2166669

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.