Strong Lyapunov Functions for Systems Satisfying the Conditions of La Salle
- 14 June 2004
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 49 (6) , 1026-1030
- https://doi.org/10.1109/tac.2004.829640
Abstract
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 presented in a previous paper that was valid only for homogeneous systems.Keywords
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