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Stability of switched systems: a Lie-algebraic condition

✍ Scribed by Daniel Liberzon; João P. Hespanha; A.Stephen Morse

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
94 KB
Volume
37
Category
Article
ISSN
0167-6911

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✦ Synopsis

We present a su cient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We also discuss the implications of this result for switched nonlinear systems.

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