RATIONAL MATRIX GCDS AND THE DESIGN OF SQUARING-DOWN COMPENSATORS - A STATE-SPACE THEORY

A state-space construction for rational matrix greatest common divisors (GCD's) of rational transfer matrices is given. Also, it is shown how the GCD results can be used to solve the problem of designing stable minimum-phase squaring-down compensators for multivariable plants. One application is a direct state-space construction for such compensators and a state-space solution to "fat-plant" H-infinity control problems. The results make use of the concepts of strongly observable systems and maximally unobservable systems initiated in the respective works of Silverman and of Wonham and build upon the concepts introduced in the state-space GCD extraction results for polynomial matrices of Silverman and Van Dooren.