Framework for Studying Stability of Switching Max-Plus Linear Systems

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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.
Original languageEnglish
Pages (from-to)68-74
JournalIFAC-PapersOnLine
Volume53
Issue number4
DOIs
Publication statusPublished - 2020
EventWODES 2020: 15th IFAC Workshop on Discrete Event Systems - Virtual Conference, Brazil
Duration: 11 Nov 202013 Nov 2020
https://wodes2020.eventos.ufrj.br/

Keywords

  • Discrete event systems
  • max-plus algebra
  • switching
  • stability
  • invariance

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