Observer design for switched linear systems with state jumps

An observer design for switched linear systems with state resets is proposed based on the geometric conditions for large-time observability from our recent work.Without assuming the observability of individual subsystems, the basic idea is to combine the maximal information available from each mode to obtain a good estimate of the state after a certain time interval (overwhich the switched system is observable) has passed.We first study systems where state reset maps at switching instants are invertible, in which case it is possible to collect all the observable and unobservable information separately at one time instant. One can then annihilate the unobservable component of all the modes and obtain an estimate of the state by introducing an error correction map at that time instant. However, for the systems with non-invertible jump maps, this approach needs to be modified and a recursion-based error correction scheme is proposed. In both approaches, the criterion for choosing the output injection matrices is given, which leads to the asymptotic recovery of the system state.