CONVERGENCE OF SOLUTIONS OF TIME-VARYING LINEAR SYSTEMS WITH INTEGRABLE FORCING TERM

Abstract

AbstractThe following system is considered in this paper: The primary goal is to establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) and a forcing term p(t) for all solutions to converge to the origin (0,0) as $t \to \infty $. Here, the zero solution of the corresponding homogeneous linear system is assumed to be neither uniformly stable nor uniformly attractive. Sufficient conditions are given for asymptotic stability of the zero solution of the nonlinear perturbed system under the assumption that q(t,0,0)=0.