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arXiv · 2007.02818

Framework for Studying Stability of Switching Max-Plus Linear Systems

Abhimanyu Gupta·Ton van den Boom·Jacob van der Woude·Bart De Schutter
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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.

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Abhimanyu Gupta, Ton van den Boom, Jacob van der Woude, Bart De Schutter. 2020-07-06. Framework for Studying Stability of Switching Max-Plus Linear Systems. https://arxiv.org/abs/2007.02818

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