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Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems

Abstract : In this paper we consider the problem of determining the stability properties, and in particular assessing the exponential stability, of a singularly perturbed linear switching system. One of the challenges of this problem arises from the intricate interplay between the small parameter of singular perturbation and the rate of switching, as both tend to zero. Our approach consists in characterizing suitable auxiliary linear systems that provide lower and upper bounds for the asymptotics of the maximal Lyapunov exponent of the linear switching system as the parameter of the singular perturbation tends to zero.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03668881
Contributor : Ihab Haidar Connect in order to contact the contributor
Submitted on : Monday, May 16, 2022 - 11:00:25 AM
Last modification on : Wednesday, June 8, 2022 - 12:50:08 PM

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  • HAL Id : hal-03668881, version 1
  • ARXIV : 2205.07699

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yacine Chitour, Ihab I. Haidar, Paolo Mason, Mario Sigalotti. Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems. 2022. ⟨hal-03668881⟩

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