Feedback Decoupling of Linear Multivariable Systems

In this paper, the decoupling problem of linear multivariable systems using a static state feedback is considered. Two main contributions related to this problem are presented. The first one is a complete characterization of the decoupled closed-loop structure of a decouplable square linear system, along with the necessary and sufficient conditions for the internal stability of the decoupled closed-loop system. The second contribution is a result presenting necessary and sufficient conditions for a right invertible linear system to be decouplable with a desirable infinite structure using nonregular state feedback. These conditions are stated in terms of the row image of two real matrices, which are obtained using the extended interactor of the system and the desirable infinity structure of the closed-loop system. A procedure is provided to find a realizable full column rank compensator that solves the problem. Given a system satisfying these conditions, it is shown how to obtain a non regular static state feedback that decouples the system.