On the stability of unsteady motions

A generalization of the fundamental Lyapunov and Chetayev theorems in which the requirement of the existence of an infinitely small upper limit for the Lyapunov function is relaxed, is presented. The generalized theorems prove that it is sufficient for Lyapunov's function either to admit of the...

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Bibliographic Details
Published inJournal of applied mathematics and mechanics Vol. 50; no. 1; pp. 40 - 45
Main Author Il'in, A.I.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 1986
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Summary:A generalization of the fundamental Lyapunov and Chetayev theorems in which the requirement of the existence of an infinitely small upper limit for the Lyapunov function is relaxed, is presented. The generalized theorems prove that it is sufficient for Lyapunov's function either to admit of the infinitely small upper limit, or to be bounded with respect to time t in certain time intervals t i for which the condition ∑ i t i → ∞ holds as t → ∞. Theorems on stability and instability are formulated to a first approximation. The application of the theorems is illustrated by the example of the stability of a second-order system, with the construction of a Lyapunov generalized function.
ISSN:0021-8928
0021-8928
DOI:10.1016/0021-8928(86)90055-9