A Local Hybrid Observer for a Class of Hybrid Dynamical Systems with Linear Maps and Unknown Jump Times

We propose a local observer design for hybrid systems with linear flow, jump, and output maps, whose jump times are not known/detected. Assuming the solutions of interest admit a dwell-time, evolve in a compact set, and the pair of flow/output maps is observable allows us to use a sufficiently fast linear observer during flow and trigger the observer jumps when its estimate reaches the jump set. However, since, as we show, using the plant output around the jump times is actually counterproductive, we propose to "disconnect" the correction term of the observer around the jump times and let the estimate flow in open-loop with the plant flow map. Local attractivity of an appropriate zero-error set is then shown for the obtained observer and illustrated in simulations.