Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems
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 p...
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| Veröffentlicht in: | Automatica (Oxford) 2023-09, Vol.155, p.111151, Article 111151 |
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| creator | Chitour, Yacine Haidar, Ihab Mason, Paolo Sigalotti, Mario |
| description | 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. |
| doi_str_mv | 10.1016/j.automatica.2023.111151 |
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| subjects | Automatic Differential inclusions Dynamical Systems Engineering Sciences Exponential stability Mathematics Maximal Lyapunov exponent Singular perturbation Switching systems |
| title | Upper and lower bounds for the maximal Lyapunov exponent of singularly perturbed linear switching systems |
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