Simultaneous pole assignment of linear MIMO dynamical systems

In this short paper we show that a generic r-tuple of m input p output dynamical systems is simultaneously stabilizable (pole assignable) if r<m+p. We also derive upper bounds on the degree of the simultaneous pole assigning compensator in the case when r⩽max(m,p) and max (m,p)<r<m+p, which improve the bound obtained by Ghosh and Byrnes (1983). This paper settles an outstanding open problem on generic simultaneous stabilization and pole assignment