Framework for Studying Stability of Switching Max-Plus Linear Systems
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.
Cite
@article{arxiv.2007.02818,
title = {Framework for Studying Stability of Switching Max-Plus Linear Systems},
author = {Abhimanyu Gupta and Ton van den Boom and Jacob van der Woude and Bart De Schutter},
journal= {arXiv preprint arXiv:2007.02818},
year = {2020}
}
Comments
To appear in the conference proceedings of the IFAC Workshop on Discrete Event Systems 2020