Chapter 4 6 2.State Matrix If the real part of every eigenvalues Ais negative,that is Re()<o then lim X(t)=0 the system is stable,otherwise lim X(t)=co the system is unstable. Consider the linear time-invariant control system differential equation X(t)=AX(t)+BU(t) where Aeh(n,n),Beh(n,r),X(t)ER",U()ER'is a controlvector. A is called the system matrix（系统矩阵)in open-loop case. If the controllaw is U=-KX(t),then X(t)=(A-BK)X() So the condition of stability of the closed loop control system is that the real part of every eigenvalue of matrix(A-BK)is negative. Chapter 4 5