Feedback decoupling-controller design of 3-D systems in state space

This paper solves the input-output decoupling problem of three-dimensional (3-D) systems formulated in state-space representation. The control policy adopted is of the static state feedback type u=Kx+Nw where K, N are appropriate matrices to be determined, x is the system state vector, and w is the new input vector assumed equidimensional to the actual input vector u. The procedure derived determines K and N such that the resulting closed-loop system has a diagonal and nonsingular transfer-function matrix. The case, where only partial input-output decoupling is possible, is also considered, and the corresponding state-feedback matrices K and N are determined. The results are illustrated by simple numerical examples. The required 3-D generalization of the well known Cayley-Hamilton theorem is provided.