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Stability of planar switched systems: The nondiagonalizable case
1. | LMDAN-LGDA Dept. de Mathématiques et Informatique, UCAD, Dakar-Fann, Senegal |
2. | Le2i, CNRS, Université de Bourgogne, B.P. 47870, 21078 Dijon Cedex, France |
This problem was solved in previous works under the assumption that both $A$ and $B$ are diagonalizable. In this paper we conclude this study, by providing a necessary and sufficient condition for asymptotic stability in the case in which $A$ and/or $B$ are not diagonalizable.
To this purpose we build suitable normal forms for $A$ and $B$ containing coordinate invariant parameters. A necessary and sufficient condition is then found without looking for a common Lyapunov function but using "worst-trajectory" type arguments.
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