Observer Design for Hybrid Dynamical Systems with Approximately Known Jump Times

Pauline Bernard (1) , Ricardo Sanfelice (2)

1 CAS - Centre Automatique et Systèmes
2 UCSC Department of Computer Engineering - Computer Engineering Department

This paper proposes a general framework for the state estimation of plants modeled as hybrid dynamical systems with discrete events (or jumps) occurring at (approximately) known times. A candidate observer consists of a hybrid dynamical system with jumps triggered when the plant jumps. With some information about the time elapsed between successive jumps, a Lyapunov-based analysis allows us to derive sufficient conditions for the design of the observer that renders the zero-estimation set uniformly asymptotically stable. The proposed sufficient conditions assure such properties when the observer has innovation terms in both the continuous regime (or flows) and at jumps, only at jumps, and also only during flows. These conditions apply to a large class of hybrid systems, including cases where the time between successive jumps is unbounded or tends to zero - namely, Zeno behavior-, as well as cases where detectability only holds during flows, at jumps, or neither. Building from these sufficient conditions, we study the robustness of this approach when the jumps of the observer are delayed with respect to those of the plant. Under some regularity and dwell-time conditions, we show that the estimation error remains bounded and satisfies a semi-global practical asymptotic stability-like property. The results are illustrated in several examples and applied to switched systems with state-triggered switches.

Mots clés: hybrid systems; impulsive systems; observer

Domaines: Systèmes dynamiques [math.DS]; Automatique / Robotique

Pauline Bernard, Ricardo Sanfelice. Observer Design for Hybrid Dynamical Systems with Approximately Known Jump Times. 2020. ⟨hal-02187411v3⟩