Observer design for hybrid dynamical systems with approximately known jump times

This paper proposes a general framework for state estimation of systems modeled as hybrid dynamical with jumps occurring at (approximately) known times. A candidate observer is system triggered when the jumps. With some information about time elapsed between successive jumps, Lyapunov-based analysis allows us to derive sufficient conditions design. In particular, high-gain flow-based observer, innovation during flow only, can be designed an average dwell-time dynamics are strongly differentially observable. On other hand, persistent, jump-based should based on equivalent discrete-time corresponding discretized jump context linear maps, this reasoning leads Kalman filter. These designs apply large class systems, including cases where unbounded or tends zero – namely, Zeno behavior–, and detectability only holds flows, neither. We also study robustness approach delayed respect those system. Under regularity conditions, we show that error semiglobally practically asymptotically stable over intervals after such delays. The results illustrated in examples applications, mechanical impacts, spiking neurons, switched systems.