Stability of linear time-varying systems†

†Communicated by the Authors.

Abstract

It is shown that Lyapunov functions similar to the Ralston-Parks and Kalman-Bertram forms (which wore employed to derive the Routh-Hurwitz conditions through Lynpunov theory) can be formed from the time-varying coefficients of time-varying differential equations for the study of stability. These Lyapunov functions are used to conclude asymptotic stability of solutions of differential equations whoso time-varying coefficients approach constant values as time tends to infinity.

Notes

†Communicated by the Authors.