Framework for Studying Stability of Switching Max-Plus Linear Systems

Journal article (2020)

Authors

A. Gupta Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
A.J.J. van den Boom Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
J.W. van der Woude Mathematical Physics - EEMCS
B.H.K. De Schutter Team Bart De Schutter - Mechanical, Maritime and Materials Engineering
Research Group
Team Bart De Schutter (Mechanical, Maritime and Materials Engineering) (TU Delft)
Copyright: © 2020 A. Gupta, A.J.J. van den Boom, J.W. van der Woude, B.H.K. De Schutter
DOI: https://doi.org/10.1016/j.ifacol.2021.04.008
Max-plus algebra Stability Switching Discrete event systems Invariance
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Published Date

2020

Language

English

Faculty

Mechanical, Maritime and Materials Engineering

Department

Delft Center for Systems and Control

Research Group

Team Bart De Schutter

Abstract

We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus algebra. Then we show the loss of equivalence of these notions for switching max-plus linear systems due to the lack of global monotonicity and the accompanying difficulty in rigorous analysis. This serves as a motivation to relax the assumption on monotonicity of the dynamics to positive invariance of max-plus cones. Then we proceed to generalise the notions of stability when the dynamics is restricted to such cones. The stability analysis approach presented in this paper serves as a first step to study the stability of a general class of switching max-plus linear systems.