Framework for Studying Stability of Switching Max-Plus Linear Systems

Reference

A. Gupta, T. van den Boom, J. van der Woude, and B. De Schutter, "Framework for studying stability of switching max-plus linear systems," Proceedings of the 15th IFAC Workshop on Discrete Event Systems (WODES 2020), Virtual conference, pp. 68-74, Nov. 2020.

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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BibTeX

@inproceedings{Gupvan:20-010,
   author    = {Gupta, Abhimanyu and van den Boom, Ton and van der Woude, Jacob
                and De Schutter, Bart},
   title     = {Framework for Studying Stability of Switching Max-Plus Linear
                Systems},
   booktitle = {Proceedings of the 15th IFAC Workshop on Discrete Event Systems
                (WODES 2020)},
   address   = {Virtual conference},
   pages     = {68--74},
   month     = nov,
   year      = {2020}
   }

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