Method of Lyapunov functions in problems of stability of solutions of systems of differential equations with impulse action

Journal Article · Fri Oct 31 00:00:00 EST 2003 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2003V194N10ABEH000776; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21208358

Ignat'yev, A O ^[1]

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1. Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Donetsk (Ukraine)

A system of ordinary differential equations with impulse action at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse actions are obtained under which the uniform asymptotic stability of the zero solution of the 'unperturbed' system implies the uniform asymptotic stability of the zero solution of the 'perturbed' system.

• OSTI ID: 21208358
• Journal Information: Sbornik. Mathematics, Vol. 194, Issue 10; Other Information: DOI: 10.1070/SM2003v194n10ABEH000776; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DIFFERENTIAL EQUATIONS
FUNCTIONS
LYAPUNOV METHOD
PERTURBATION THEORY
STABILITY