Stability of moving invariant sets. (English) Zbl 0947.34039

Lakshmikantham, V.; Vatsala, A. S.

Sivasundaram, S. (ed.) et al., Advances in nonlinear dynamics. Langhorne, PA: Gordon and Breach. Stab. Control Theory Methods Appl. 5, 79-83 (1997).

The authors consider nonlinear continuous-time systems with an uncertain (changing) parameter vector. Hence, equilibria and other invariant sets vary with changes of the parameter. To investigate the stability of the moving invariant sets, the generalized derivative of the Lyapunov function must be estimated from opposite directions relative to suitable sets in the phase space that depend on the moving parameter. The given problem is reduced to a simpler comparison problem what results in a Lyapunov-type criterion. Discussions are based on a special situation. Unfortunately, a concrete example is missing.
For the entire collection see [Zbl 0905.00028].

Reviewer: Inge Troch (Wien)

MSC:

34D05	Asymptotic properties of solutions to ordinary differential equations
34D45	Attractors of solutions to ordinary differential equations

Keywords:

equilibria; invariant sets; generalized derivative; Lyapunov function