Stability for impulsive differential systems in terms of two measures. (English) Zbl 0669.34056

Lakshmikantham, V.; Liu, Xinzhi

Appl. Math. Comput. 29, No. 1, 89-98 (1989).

Using different measures for the “deviations” of the initial value and the value at the moment t of a solution, the authors introduce new concepts of stability for impulsive differential systems. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability in this new sense are established by the aid of Lyapunov functions, which are assumed to be piecewise continuous. The theorems have interesting corollaries involving and improving a variety of stability results found in the literature.

Reviewer: L.Hatvani

MSC:

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

Keywords:

impulsive differential systems; uniform stability; asymptotic stability; uniform asymptotic stability; Lyapunov functions

References:

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