A General Survey of the Methods of Constructing Lyapunov Functions for Non-Linear Systems (Obshchii obzor Metodov Postroeniya Funktsii Lyapunova dlya Nelineinykh Sistem),
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 02, 1972
- Accession Number
- AD0745530
Entities
People
- E. A. Barbashin
Organizations
- United States Army Foreign Science and Technology Center