A transfer matrix approach to feedback invariants of linear systems: Application to decoupling

AbstractThe transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups. These transformation groups include the classical state feedback, state, and input changes of coordinates. Then the solvability of numerous classical control problems (e.g. decouplability, disturbance rejection, model following) can be expressed directly in terms of these invariants. In this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems. These invariants turn out to be crucial in studying feedback decoupling problems. The main tools for this study are factorization of transfer matrices over the P.I.D. of proper rational functions. When dealing with stability we factor transfer matrices over the P.I.D. of proper rational stable functions. We illustrate the use of these invariants by studying some decoupling problems