Coupling Flow and Jump Observers for Hybrid Systems with Known Jump Times

This work presents a novel observer design methodology for general hybrid systems with known jump times. We propose to combine a high-gain flow-based observer estimating the part of the state that is instantaneously observable from the flow output, with a jump-based observer estimating the rest of the state from the knowledge of the jump output as well as some additional fictitious outputs, describing how the instantaneously observable part of the state impacts the non-observable one at jumps. We give general Lyapunov-based sufficient conditions for coupling such observers and propose an observer design for a large class of hybrid systems with nonlinear maps covering mechanical systems with uncertain impact models. Application to a bouncing ball with an unknown restitution coefficient illustrates the proposed approach.