Lyapunov Stability of Systems of Linear Generalized Ordinary Differential Equations

摘要

Effective necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of the linear system of generalized ordinary differential equations dx(t) = dA(t)·x(t) + df(t), where A: R_+ → R~(n x n) and f: R_+ ? R~n (R_+ = [0, +∞[) are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from R_+, having properties analogous to the case of systems of ordinary differential equations with constant coefficients. The obtained results are realized for linear systems of both impulsive equations and difference equations.