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. 

Figures and Topics from this paper.

Explore Further: Topics Discussed in This Paper

Citations

Publications citing this paper.
SHOWING 1-10 OF 23 CITATIONS

Stability and Optimal Control of Switching PDE-Dynamical Systems

VIEW 9 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

A non-coercive Lyapunov framework for stability of distributed parameter systems

  • 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
  • 2017
VIEW 3 EXCERPTS
CITES BACKGROUND & RESULTS
HIGHLY INFLUENCED

Control of Hyperbolic Systems by Lyapunov Analysis

VIEW 3 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-10 OF 29 REFERENCES

Converse Lyapunov theorems for switched systems in Banach spaces

Falk M. Hante, Mario Sigalotti
  • In Proceedings of the 49th IEEE Conference on Decision and Control,
  • 2010
VIEW 3 EXCERPTS
HIGHLY INFLUENTIAL

Lyapunov functions that specify necessary and sufficient conditions for absolute stability of nonlinear nonstationary control

Alexandre P. Molchanov, Ye. S. Pyatnitskiy
  • Remote Control,
  • 1986
VIEW 4 EXCERPTS
HIGHLY INFLUENTIAL

Sontag , and Yuan Wang . A smooth converse Lyapunov theorem for robust stability

Yuandan Lin, D Eduardo
  • IEEE Trans . Automat . Control
  • 2009

Similar Papers

Loading similar papers…