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Controllability of singular control systems with delay. (Chinese) Zbl 0967.93010

The authors deal with the controllability of singular control systems with delay. Several necessary and sufficient conditions for the controllability are given, which are similar to those for regular control systems. For example, one of them is that the system Nx ˙(t)=x(t)+Bx(t-1)+Cu(t), where x n , B n×n , C n×m , u m is completely controllable for t[t 0 +k,t 0 +k+1), k is an integer, if and only if the matrix J k =(A 0 ,A 1 ,,A k ), where

A n =(B j,0 C,B j,1 C,,B j,(j+1)(j-1) C),B j,n = k=0 n N k B j-1,n-k ,

has full rank.

93C23Systems governed by functional-differential equations