Definitions of incremental stability for hybrid systems

Conference paper (2015)

Authors

R. Postoyan Lorraine University
J. Biemond Katholieke Universiteit Leuven
W. P.M.H. Heemels Eindhoven University of Technology
N. van de Wouw Team Bart De Schutter - Mechanical, Maritime and Materials Engineering , Eindhoven University of Technology
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Convergence Stability analysis Euclidean distance Time-domain analysis Asymptotic stability Discrete-time systems Hybrid power systems
More Info
expand_more

Published Date

2015

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

The analysis of incremental stability properties typically involves measuring the distance between any pair of solutions of a given dynamical system, corresponding to different initial conditions, at the same time instant. This approach is not directly applicable for hybrid systems in general. Indeed, hybrid systems generate solutions that are defined with respect to hybrid times, which consist of both the continuous time elapsed and the discrete time, that is the number of jumps the solution has experienced. Two solutions of a hybrid system do not a priori have the same time domain, and we may therefore not be able to compare them at the same hybrid time instant. To overcome this issue, we invoke graphical closeness concepts. We present definitions for incremental stability depending on whether incremental asymptotic stability properties hold with respect to the hybrid time, the continuous time, or the discrete time, respectively. Examples are provided throughout the paper to illustrate these definitions, and the relations between these three incremental stability notions are investigated. The definitions are shown to be consistent with those available in the literature for continuous-time and discrete-time systems.