On the observer design problem for continuous-time switched linear systems with unknown switchings

The observer design problem for Switched Linear Systems (SLS) subject to an unknown switching signal is addressed in this work. Based on known observability results for SLS, an appropriate SLS observer is proposed and its convergence is analysed showing that the corresponding estimates converge in finite-time to the SLS state. More precisely, the observers of the continuous state evolution and the observers of the switching signal are investigated and their convergence studied separately. The main tool to analyse the observability is the well-known geometric concept of (A, B)-invariant subspaces. The developed SLS observers are then applied to construct synchronized chaotic generators based on the SLS with chaotic behavior. Finally, an example of a non-trivial chaotic SLS and its detailed analysis are presented to illustrate the achieved results.