具有时滞的线性时变大系统的平稳振荡

本文运用Schauder不动点原理给出了具有时滞的线性周期耗散大系统 (dx(t))/(dt)=C(t)x(t)+B(t)x(t-τ)+f(t)(τ≥0) (1)存在一个平稳振荡的充分条件。

OSCILLATION IN A STATE OF STABILITY OF LINEAR LARGE SYSTEM WITH DELAY

The existence of oscillation in a state of stability of dx/dt=A(t)x + g(t) (2) has been discussed in [1], [2], and [3]、 This paper aims to establish a sufficient condition of existence, uniqueness, and stability of periodic solution with period ω of dx(t)/dtC(t)x(t)+B(t)x(t-τ) +f(t) (1) using the Liapunov funetion's analytic method and Schauder's fixed point principle, For system(1), the authors have provided the slowly varible bownd of subsystem, boundary of value region of correlation, and subbound for time lagτ, All of the estimated formulas are more convenient to use in practical engineering or physics.