Denominator Assignment, Invariants and Canonical Forms Under Dynamic Feedback Compensation in Linear Multivariable Systems

A result orinally reported by Hammer

for linear time invariant (LTI) single input-single output systems and concerning an invariant and a canonical form of the transfer function matrix of the closed loop system under dynamic feedback compensation is generalized for LTI multivariable systems. Based on this result, we characterize the class of transfer function matrices that are obtainable from an open loop transfer function matrix via the use of proper dynamic feedback compensators and show that if the closed loop transfer function matrix
$P_{c}(s)$
has a desired denominator polynomial matrix which satisfies a certain sufficient condition, then there exists a proper compensator giving rise to an internally stable closed loop system, whose transfer function matrix is
$P_{c}(s)$
.