Generalized direct Lyapunov method for the analysis of stability and attraction in general time systems

Journal Article · Thu Oct 31 00:00:00 EST 2002 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2002V193N10ABEH000684; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21205723

Druzhinina, O V; Shestakov, A A ^[1]

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1. Moscow State University of Railway Engineering, Moscow (Russian Federation)

A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system.

• OSTI ID: 21205723
• Journal Information: Sbornik. Mathematics, Vol. 193, Issue 10; Other Information: DOI: 10.1070/SM2002v193n10ABEH000684; 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
FUNCTIONS
LYAPUNOV METHOD
STABILITY