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# Stability of uniformly bounded switched systems and Observability

Abstract : This paper mainly deals with switched linear systems defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function. Its aim is to give sufficient conditions for such a system to be GUAS. We show that this property of being GUAS is equivalent to the uniform observability on $[0,+\infty)$ of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switched system. Some sufficient conditions of uniform asymptotic stability are then deduced from the equivalence theorem, and illustrated by examples. The results are partially extended to nonlinear analytic systems.
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Journal articles

Cited literature [15 references]

https://hal.archives-ouvertes.fr/hal-00661224
Contributor : Philippe Jouan Connect in order to contact the contributor
Submitted on : Saturday, September 19, 2015 - 6:01:20 PM
Last modification on : Wednesday, November 3, 2021 - 8:14:34 AM
Long-term archiving on: : Tuesday, December 29, 2015 - 8:49:16 AM

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Switch&Obs LnL.pdf
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### Citation

Moussa Balde, Philippe Jouan, Said Naciri. Stability of uniformly bounded switched systems and Observability. Acta Applicandae Mathematicae, Springer Verlag, 2016, ⟨10.1007/s10440-015-0039-9⟩. ⟨hal-00661224v2⟩

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