On the stability of acting force of linear systems of differential equations with changeable coefficients

The problem of stability depending on acting force of the system of the linear differential equations with changeable coefficients is considered. It is shown that Liapunov’s reconstruction equivalence of tasks of stability depending on acting force of systems with changeable and with constant coefficients is preserved. Necessary and sufficient conditions are obtained, under which the resulted system of the linear differential equations with changeable coefficients is stable, asymptotic stable or unstable depending on acting force.