Robust estimation of linear switched systems with dwell time

Abstract

A covariance analysis is introduced for linear switched systems with dwell time constraints. This analysis reduces the conservatism that is encountered in the analysis of switched systems without dwell. An upper-bound on the covariance of the states of the switched system is obtained that depends on the switching signal. The obtained results are then applied to filtering problems in switched systems with driving and measurement with noise signals, where general type filters are considered. These filters assume that the switching signal is not given a priori but it is available in real time. In order to overcome the deficiencies of the standard approaches to robust filtering of systems with large parameter uncertainties, we also present a new method of estimation for non-switched, exponentially stable, uncertain systems. We divide the uncertainty region into several overlapping sub-regions where, for each of these sub-regions, a separate filter should be assigned. The resulting system is then treated as a switched system that switches between the sub-regions. The theory developed is demonstrated by two simple examples. In the first, a filtering solution is obtained for a switched system with error variance that is very close to the best achievable result for a single subsystem. The second example demonstrates the benefit, from the estimation error point of view, of dividing the uncertainty polytope of an uncertain non-switched system into two overlapping subpolytopes.

Keywords:

• linear switched systems
• robust H ₂ filtering
• dwell time
• polytopic uncertainties

Acknowledgements

This work was supported by the C&M Maus Chair at Tel Aviv University.