Accession Number : AD0745530

Title :   A General Survey of the Methods of Constructing Lyapunov Functions for Non-Linear Systems (Obshchii obzor Metodov Postroeniya Funktsii Lyapunova dlya Nelineinykh Sistem),

Corporate Author : ARMY FOREIGN SCIENCE AND TECHNOLOGY CENTER CHARLOTTESVILLE VA

Personal Author(s) : Barbashin,E. A.

Report Date : 02 JUN 1972

Pagination or Media Count : 25

Abstract : Several methods of constructing Lyapunov functions are discussed. It is noted that for any system of differential equations any positive definite function v may serve as a Lyapunov function. A criterion for evaluation of Lyapunov functions is given: the sufficient conditions obtained with the help of this function in the non-linear case must also be necessary in the linear case. Lyapunov functions in relation to Routh-Hurwitz conditions are discussed, as is, inter alia, the energetic method of constructing Lyapunov functions: here Lyapunov functions are used to describe the effects of the application of mechanical energy to a conservative system with a known total kinetic and potential energy. The suitability of Lyapunov functions in regard to systems amounting to physical models of systems of differential equations is discussed. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, NONLINEAR SYSTEMS), CONTROL SYSTEMS, MATHEMATICAL MODELS, FUNCTIONS(MATHEMATICS), STABILITY, USSR

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE