Interval centred form for proving stability of non-linear discrete-time systems

Auguste Bourgois
(ENSTA Bretagne, Brest, France)
Luc Jaulin
(ENSTA Bretagne, Brest, France)

In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and makes it possible to easily prove asymptotic stability of a discrete system. Then, we illustrate the principle of our approach through theoretical examples. Finally, we provide two practical examples using our method : proving stability of a localisation system and that of the trajectory of a robot.

In Thao Dang and Stefan Ratschan: Proceedings 6th International Workshop on Symbolic-Numeric methods for Reasoning about CPS and IoT (SNR 2020), online, 31 August 2020, Electronic Proceedings in Theoretical Computer Science 331, pp. 1–17.
Published: 11th January 2021.

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