On the flexibility offered by state feedback in multivariable systems beyond closed loop eigenvalue assignment

Abstract

In the first part of the paper, a characterization is given for the class of all closed loop eigenvector sets which can be obtained with a given set of distinct closed loop eigenvalues using state feedback. It is shown, furthermore, that the freedom one has in addition to specifying the closed loop eigenvalues is precisely this: to choose one set of closed loop eigenvectors from this class. Included in the proof of this result is an algorithm for computing the matrix of feedback gains which gives the chosen closed loop eigenvalues and eigenvectors. The last few sections of the paper present a method of utilizing the freedom to choose closed loop eigenvectors to improve the transient response characteristics of a coupled setpoint control system without altering its eigenvalues.