Construction and applications of the matrix-valued Liapunov functions for some quasi-periodic systems

Abstract

One of the ways of constructing Liapunov’s matrix-valued function for the system of differential equations with quasi-periodical coefficients has been proposed. On the basic of this function conditions of asymptotic stability of some classes of linear and non-linear systems have been established. The way of constructing of Liapunov’s function is subordinated to the basic theorem about asymptotic stability on the base of matrix function. The simplest quasi-periodical functions are considered as the quasi-periodical coefficients. They are trigonometric polynomials. The constructibility for some classes of the systems of the function was proposed has been affirmed by examples.