On universal classes of Lyapunov functions for linear switched systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2022
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| _version_ | 1866914836829437952 |
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| author | Mason, Paolo Chitour, Yacine Sigalotti, Mario |
| author_facet | Mason, Paolo Chitour, Yacine Sigalotti, Mario |
| contents | In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the $C^0$ topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous functions whose construction involves at most $l$ polynomials of degree at most $m$ (for given positive integers $l,m$) cannot be universal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09179 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On universal classes of Lyapunov functions for linear switched systems Mason, Paolo Chitour, Yacine Sigalotti, Mario Optimization and Control In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it approximates arbitrarily well every convex absolutely homogeneous function for the $C^0$ topology of the unit sphere. On the other hand, we prove several obstructions for a class to be universal, showing, in particular, that families of piecewise-polynomial continuous functions whose construction involves at most $l$ polynomials of degree at most $m$ (for given positive integers $l,m$) cannot be universal. |
| title | On universal classes of Lyapunov functions for linear switched systems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2208.09179 |