Title :
A necessary condition for local asymptotic stability of equilibria of nonlinear systems with parameters
Author :
Byrnes, Christopher I. ; Sundarapandian, Vaidyanathan
Author_Institution :
Dept. of Syst. Sci. & Math., Washington Univ., St. Louis, MO, USA
Abstract :
We derive a necessary condition for local asymptotic stability of equilibria of nonlinear systems with parameters. As a corollary of our general result, we deduce Brockett´s necessary condition (1983) for local asymptotic stability of equilibria of nonlinear autonomous systems. We show by way of an example that our necessary condition is stronger than Brockett´s necessary condition, but retains much of the user-friendly appeal of Brockett´s criterion. We further illustrate our result with more examples
Keywords :
asymptotic stability; differential equations; nonlinear control systems; robust control; local asymptotic stability; necessary condition; nonlinear autonomous systems; Asymptotic stability; Bifurcation; Control systems; Differential equations; Eigenvalues and eigenfunctions; Lyapunov method; Mathematics; Nonlinear systems; Robust control; Robust stability;
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.1999.833384
