On minimal degree simultaneous pole assignment problems

In this paper, we show that a generic 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. We also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r-tuple of closed loop systems. The upper bounds are obtained for each of the two cases r≤max(m,p) and max(m,p)<r<m+p.