Cím: | On the asymptotic stability by Lyapunov function with semidefinite derivative. |
Szerző: | Hatvani, L. |
Forrás: | Trends in theory and practice of nonlinear differential equations, Proc. int. Conf., Arlington/Tex. 1982, Lect. Notes Pure Appl. Math. 90, 247-253 (1984). |
Nyelv: | English |
Absztrakt: | [For the entire collection see Zbl 0519.00009.] \par
Sufficient
conditions for the asymptotic stability and partial asymptotic
stability of the zero solution of a differential system are given
by the use of Lyapunov's direct method. In nonautonomous case
the derivative of the Lyapunov function is assumed to be estimated:
\.V(t,x)$\le - \phi(t)U(x)$, where $\phi$ (t) is integrally positive
or weakly integrally positive, U(x) positive semidefinite. \par
By
the help of the method of limiting equation a sufficient condition
for the partial asymptotic stability of the zero solution of
an autonomous system is found without requiring boundedness of
the uncontrolled coordinates. The results are applied to the
study of stability properties of equilibria in mechanical systems
being under the action of dissipative forces. |
Letöltés: | | Zentralblatt |