Framework for Studying Stability of Switching Max-Plus Linear Systems. Issue 4 (2020)

• Record Type: Journal Article
• Authors: Gupta, Abhimanyu; Boom, Ton van den; Woude, Jacob van der; Schutter, Bart De
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 4(2020)
• Page Start: 68
• Page End: 74
• Publication Date: 2020
• Subjects: Discrete event systems -- max-plus algebra -- switching -- stability -- invariance; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.04.008
• Languages: English
• ISSNs: 2405-8963

Abstract

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.