三阶直接控制系统绝对稳定的充分必要条件

来源期刊：中南大学学报(自然科学版)2004年第3期

论文作者：刘波 张孟秋

文章页码：518 - 522

关键词：直接控制系统;绝对稳定性;充分必要条件

Key words：direct control system; absolute stability; necessary and sufficient condition

摘    要：利用popov频率法,讨论了三阶直接控制系统d_X/d_t=AX+bf(σ),σ= c^TX零解的绝对稳定性,获得了A在c^Tb·trA²-c^TA²b≤0的条件下,其零解绝对稳定的充分必要条件为c^Tb≤0, c^TA^-1b≥0;特别是当A=diag(-ρ₁,-ρ₁,-ρ₂)时,零解绝对稳定的充分必要条件为c^Tb≤0, c^TA^-1b≥0。

Abstract: In this paper, the absolute stability of 3-rd order direct control system d_X/d_t=AX+bf(σ),σ= c^TX is discussed by means of Popov frequency method. The main results are: ifA=(aij)_3×3, Reλ(A)<0, and c^Tb·trA²-c^TA²b≤0, the necessary and sufficient condition for absolute stability of the system is that c^Tb≤0, c^TA^-1b≥0; especially when A=diag(-ρ₁,-ρ₁,-ρ₂), the necessary and sufficient condition for absolute stability of the system is c^Tb≤0, c^TA^-1b≥0.