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arXiv · 2012.06924

Stability of Stochastically Switched and Stochastically Time-Delayed Systems

Camille Carter·Jacob Murri·David Reber·Benjamin Webb
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Abstract

In this paper we introduce the notion of a patient first-mean stable system. Such systems are switched systems that are first-mean stable meaning that they converge to a globally attracting fixed point on average. They are also patient so that they do not lose their first-mean stability when time-delays are introduced into the system. As time-delays are, in general, a source of instability and poor performance patient first-mean stability is a much stronger condition than first-mean stability. This notion of patient stability allows one to design systems that cannot be destabilized via time-delays. It also significantly reduces the difficulty of modeling such systems since in patient systems time-delays can, to a large extent, be safely ignored. The paper's main focus is on giving a sufficient criteria under which a system is patient first-mean stable and we give a number of examples that demonstrate the simplicity of this criteria.

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Camille Carter, Jacob Murri, David Reber, Benjamin Webb. 2020-12-13. Stability of Stochastically Switched and Stochastically Time-Delayed Systems. https://arxiv.org/abs/2012.06924

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