The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances

Necessary and sufficient conditions are derived for a minimal order linear time-invariant differential feedback control system to exist for a linear time-invariant multivariable system with unmeasurable arbitrary disturbances of a given class occurring in it, such that the outputs of the system asymptotically become equal to preassigned functions of a given class of outputs, independent of the disturbances occurring in the system, and such that the closed-loop system is controllable. The feedback gains of the control system are obtained so that the dynamic behavior of the closed-loop system is specified by using either an integral quadratic optimal control approach or a pole assignment approach. The result may be interpreted as being a generalization of the single-input, single-output servomechanism problem to multivariable systems or as being a solution to the asymptotic decoupling problem.