Arbitrary Assignment of Eigenvectors With State Feedback

Abstract

Conditions under which eigenvectors of linear multivariable systems can be arbitrarily assigned using state feedback are derived. A procedure for obtaining the required feedback gain matrix is also given. Embedded within the procedure is the freedom to minimize the gain matrix as well as select eigenvalues associated with the assigned eigenvectors. Consequently, arbitrary shaping of the system transient response is possible by concentrating system energy in specific modes. This technique is well suited for applications in the active vibration control of mechanical systems.