Analysis of stability problems via matrix Lyapunov functions. (1990)

• Record Type: Journal Article
• Authors: Martynyuk, Anatoly A.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 3:Number 4(1990)
• Page Start: 209
• Page End: 226
• Publication Date: 1990
• Subjects: Lyapunov matrix function -- stability -- asymptotic stability -- nonlinear systems; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S104895339000020X
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : The stability of nonlinear systems is analyzed by the direct Lyapunov's method in terms of Lyapunov matrix functions. The given paper surveys the main theorems on stability, asymptotic stability and nonstability. They are applied to systems of nonlinear equations, singularly-perturbed systems and hybrid systems. The results are demonstrated by an example of a two-component system.