Electronic Resource
Springer
Journal of optimization theory and applications
80 (1994), S. 149-160
ISSN:
1573-2878
Keywords:
Stability of dynamical systems
;
Liapunov function
;
positive-definite Liapunov functions
;
level sets
;
Jordan curves
;
Clarke derivatives
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract As is well known, the stability of a dynamical system in two dimensions may be demonstrated in a very intuitive fashion from the existence of a suitable positive-definite Liapunov function, providing the contours of this function in a neighborhood of the stable point are Jordan curves. It is shown that the Liapunov function will certainly have this property if the stable point is an isolated stationary point in the sense of the Clarke calculus, but a counterexample is given if this assumption is weakened to the stable point being an isolated local extremum.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02196598
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