On minimal degree simultaneous pole assignment problems (Q1611912)

The main objective of this paper is to find the smallest possible integer \(q\) such that the closed-loop characteristic polynomials of a generic \(r\)-tuple of linear systems of degrees \(n_1,\dots, n_r\), respectively, can be arbitrarily assigned by a single dynamic compensator of degree not exceeding \(q\). It is shown that such an \(r\)-tuple of \(m\)-input \(p\)-output linear systems is simultaneously pole assignable if \(r< m+p\) and the McMillan degrees of the systems are not too different. Upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the \(r\)-tuple of closed-loop systems are also obtained. The upper bounds are obtained for each of the two cases \(r\leq \max(m,p)\) and \(\max(m,p)< r< m+p\).