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Controllability of singular control systems with delay. (Chinese. English summary) 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 \(N\dot x(t)= x(t)+ Bx(t-1)+ Cu(t)\), where \(x\in\mathbb{R}^n\), \(B\in \mathbb{R}^{n\times n}\), \(C\in \mathbb{R}^{n\times m}\), \(u\in \mathbb{R}^m\) is completely controllable for \(t\in [t_0+ k,t_0+ k+1)\), \(k\) is an integer, if and only if the matrix \(J_k= (A_0,A_1,\dots, A_k)\), where \[ A_n= (B_{j,0}C, B_{j,1}C,\dots, B_{j,(j+1)(j-1)}C),\quad B_{j,n}= \sum^n_{k=0} N^k B_{j-1,n-k}, \] has full rank.
Reviewer: Daoyi Xu (Chengdu)

MSC:

93B05 Controllability
93C23 Control/observation systems governed by functional-differential equations
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