Stability of sets for systems with impulses. (English) Zbl 0684.34053

Kulev, G. K.; Bainov, D. D.

Bull. Inst. Math., Acad. Sin. 17, No. 4, 313-326 (1989).

Summary: Some problems related to stability and asymptotical stability of sets of sufficiently general type with respect to systems with impulses are considered. The research is done by means of piecewise continuous auxiliary functions which are an analogue of the classical Lyapunov’s functions. It is proved that the existence of such functions with certain properties is a sufficient condition for various types of stability and asymptotical stability of sets with respect to systems with impulses.

MSC:

34D20	Stability of solutions to ordinary differential equations
34D05	Asymptotic properties of solutions to ordinary differential equations

Keywords:

asymptotical stability; Lyapunov’s functions; systems with impulses