journal6 ›› 2005, Vol. 26 ›› Issue (1): 84-86.

• Mathematics • Previous Articles     Next Articles

Necessary and Sufficient Conditions for the Absolute Stability of Some 4th Order Direct Control Systems


  1. (College of Mathematical Science and Computing Technology,Central South University,Changsha 410083,Hunan China)
  • Online:2005-01-15 Published:2012-09-22

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

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