Polynomial approach to pole shifting to infinity in singular systems by feedbacks
Tadeusz Kaczorek · Bulletin of the Polish Academy of Sciences Technical Sciences · 2002
Necessary and sufficient conditions are established for the existence of a state-feedback gain matrix K such that the closed-loop characteristic polynomial is of the zero degree, det[Es - A + BK] = a ≠ 0 (a is independent of s). Necessary and sufficient conditions are also established for the existence of a solution X = In, Y = K to the polynomial matrix equation [Es - A]X + BY = U(s) for an unimodular matrix U(s)(detU(s) = α). Procedures for computation of K are proposed and illustrated by numerical examples. It is shown that the complete controllability of the system is sufficient but not necessary and the strong controllability of the system is not necessary condition for the existence of solution to the first problem.