The Minimum Number of Degrees of Freedom in State Feedback Control

A general eigenvalue assignment (EA) control problem for linear multivariable systems is formulated and solved within the framework of parametric eigenstructure assignment. It is shown that EA control is achievable by means of a family of classes of state feedback EA controllers. The number of classes is equal to the number of admissable Jordan forms of the closed-loop system. Each class is characterised by a specific minimum number N of free parameters (degrees of freedom) in the parametric form of the feedback gain matrix. The class of EA controllers with the greatest value of N is specified.