Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces

@article{Hante2011ConverseLT,
  title={Converse Lyapunov Theorems for Switched Systems in Banach and Hilbert Spaces},
  author={Falk M. Hante and Mario Sigalotti},
  journal={SIAM J. Control and Optimization},
  year={2011},
  volume={49},
  pages={752-770}
}
We consider switched systems on Banach and Hilbert spaces governed by strongly continuous one-parameter semigroups of linear evolution operators. We provide necessary and sufficient conditions for their global exponential stability, uniform with respect to the switching signal, in terms of the existence of a Lyapunov function common to all modes. 

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