Observer design for linear switched control systems

Full and reduced order observers for a class of linear switched control systems (LSCS) are studied in this paper. A "sub-observer" is first designed for the i-th subsystem. Then, a switching observer for an LSCS is constructed by simply picking the i-th sub-observer whenever the i-th subsystem is active. In the case of a full order observer, when subsystems are detectable, the state estimation error can converge to zero if the dwell time is large enough. Under certain conditions, the state estimation error may even converge to zero exponentially for arbitrary switching. Unlike classical linear systems where full order and reduced order observer can be designed under the same conditions, the design of a reduced order observer for an LSCS, besides detectability/observability, requires additional condition that the gains for all reduced order sub-observers need to be chosen the same. In such a case, similar stability results as those of full order observers are obtained for reduced order observers. Finally, examples and simulation results are given to show the effectiveness of the proposed observers.