Disturbance rejection in multivariable systems by state feedback controller

In this paper, computational algorithms for designing a state feedback controller to reject the disturbances acting on linear time-invariant multivariable systems is presented. The theoretical basis for these algorithms is a factorization procedure for the transfer function matrix between the outputs and the disturbance. This enables us to use the concept of a minimal order inverse to determine the position of the ‘disturbance blocking zeros’ which can be assigned by state feedback to desired locations, such that all measurable or unmeasurable exponential disturbances are rejected in the steady state. The performance of the algorithms are illustrated by two numerical examples.