journal6 ›› 2005, Vol. 26 ›› Issue (1): 84-86.
• 数学 • 上一篇 下一篇
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摘要:运用Popov频率法则,讨论了四阶直接控制系统的(dX)/(dt)=AX+bf(σ),σ=cTX零解的绝对稳定性,获得了(Aij)4×4在Re λ(A)<0,cT(A-1)2b≤0,cT(A4-tr A2·A2)b-1/2tr(A4-tr A2·A2)cTb≤0,cTb·tr A2-cTA2b≤0的条件下,系统零解绝对稳定的充分必要条件为cTb≤0,cTA-1b≥0.
关键词: 直接控制系统, 绝对稳定, 充分必要条件
Abstract: The absolute stability of 4th order direct control system (dx)/(dt)=Ax+bf(σ),σ=CTX is discussed by means of Popov frequency method.The main results are:(Aij)4×4 when if Re λ(A)<0,cT(A-1)2b≤0,cT(A4-tr A2·A2)b-1/2tr(A4-tr A2·A2)cTb≤0,cTb·tr A2-cTA2b≤0,the necessary and sufficient conditions for the absolute stability of the system is that cTb≤0,cTA-1b≥0.
Key words: direct control system, absolute stability, necessary and sufficient conditions
王艳群, 张孟秋, 徐慧. 四阶直接控制系统绝对稳定的充分必要条件[J]. journal6, 2005, 26(1): 84-86.
WANG Yan-Qun, ZHANG Meng-Qiu, XU Hui. Necessary and Sufficient Conditions for the Absolute Stability of Some 4th Order Direct Control Systems[J]. journal6, 2005, 26(1): 84-86.
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https://zkxb.jsu.edu.cn/CN/Y2005/V26/I1/84