Polynomials for the states and control of control systems with time delay (Q1915801)

The main result of this paper is concerned with the deadbeat control of the simple linear delay system \(\dot x = Ax (t - 1) Bu(t)\), \(x(t) = q(t)\), \(- 1 \leq t \leq 0\). It states that if \(q\) is a polynomial function (vector-valued) and \((A,B)\) is controllable then there exists a time \(T\) such that some polynomial control \(u\) drives the system to zero in the interval \(T - 1 \leq t \leq T\), i.e. \(x(t) = 0\), for \(T - 1 \leq t \leq T\) for this control. The result is extended to the multi-input, multi-output case.