Title :
On global Lyapunov functions of nonlinear autonomous systems
Author :
Wang, X.A. ; Dayawansa, W.
Author_Institution :
Dept. of Math. & Stat., Texas Tech. Univ., Lubbock, TX, USA
fDate :
6/21/1905 12:00:00 AM
Abstract :
In this paper we study a method for constructing Lyapunov functions defined on the whole region of attraction of an exponentially stable equilibrium point of nonlinear autonomous systems. The method involves solving a partial differential equation. We prove that a solution exists in the region of attraction. When the eigenvalues of the linearization of the system are non-resonant, a power series solution can be found, and its region of convergence can be used to determine the region of attraction
Keywords :
Lyapunov methods; eigenvalues and eigenfunctions; partial differential equations; series (mathematics); eigenvalues; exponentially stable equilibrium point; global Lyapunov functions; linearization; nonlinear autonomous systems; partial differential equation; power series solution; Eigenvalues and eigenfunctions; Linear systems; Lyapunov method; Mathematics; Nonlinear systems; Partial differential equations; Resonance; State-space methods; Statistics; Tiles;
Conference_Titel :
Decision and Control, 1999. Proceedings of the 38th IEEE Conference on
Conference_Location :
Phoenix, AZ
Print_ISBN :
0-7803-5250-5
DOI :
10.1109/CDC.1999.830258
