New method of parametric eigenvalue assignment in state feedback control

A new method is described for the assignment of eigenvalues of closed-loop plants in linear time-invariant multivariable systems. The parameterisation of controllers is based on the derivation of zero eigenvalue assignment by implementation of vector companion forms. This method is computationally very attractive and can be used for optimisation of the feedback matrix which assigns the closed-loop eigenvalues (from the set of real, complex conjugates or even those of the open-loop system) to the desired locations. A numerical example is presented to illustrate some advantages of this new explicit parameterisation of the controller gain matrix