Decoupling of square singular systems via proportional state feedback

Necessary and sufficient conditions for the decoupling of a solvable square singular system Ex˙(t)=Ax(t)+Bu(t ) with output y(t)=Dx(t), through an admissible control law of the form u(t)=Kx(t)+Hr(t) where H is a square nonsingular matrix. It has been shown that for a given singular system that satisfies these conditions, a propagational state feedback exists for which the system´s transfer function is a diagonal, nonsingular, and proper rational matrix. The proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback