Strong Lyapunov functions for systems satisfying the conditions of La salle

@article{Mazenc2004StrongLF,
  title={Strong Lyapunov functions for systems satisfying the conditions of La salle},
  author={Fr{\'e}d{\'e}ric Mazenc and Dragan Nesic},
  journal={IEEE Transactions on Automatic Control},
  year={2004},
  volume={49},
  pages={1026-1030}
}
We present a construction of a (strong) Lyapunov function whose derivative is negative definite along the solutions of the system using another (weak) Lyapunov function whose derivative along the solutions of the system is negative semidefinite. The construction can be carried out if a Lie algebraic condition that involves the (weak) Lyapunov function and the system vector field is satisfied. Our main result extends to general nonlinear systems the strong Lyapunov function construction… CONTINUE READING
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