A theory of modal control

Although considerable progress has been made in various aspects of control theory, there still appears to be no adequate theory for the control of large-scale linear time-invariant multivariable systems. If the engineering specifications required of the controlled system can be effectively summarized in a quadratic performance measure, then linear optimal control theory, in principle, provides a linear feedback controller which would perform the required task. Even under these circumstances the computational problems may be insurmountable. In an effort to circumvent these difficulties Rosenbrock suggested the use of modal control as a design aid. Modal control may be defined as control which changes the modes (i.e., the eigenvalues of the system matrix) to achieve the desired control objectives. This paper presents a complete and rigorous theory of modal control as well as recursive algorithms which permit modal control to be realized.