Noninteracting control with stability for unity output feedback systems: a complete solution

Abstract

We consider the block decoupling problem with internal stability for arbitrary linear time-invariant multivariable systems, using unity output feedback compensation. A necessary and sufficient condition for the solvability of this problem is given. Two new concepts, LU-factorizations and strict block adjoints of polynomial matrices, are introduced in resolution of the problem. The sets of all decoupling compensators and decoupled loop transfer function matrices are characterized. These results extend our previous work on the diagonal decoupling problem with stability for square plants. Examples are included for illustration.