S-domain solution for the fixed end-point optimal-control problem

A design procedure is described for constant linear multivariable systems that must minimise a finite time quadratic cost function and achieve a fixed terminal state. This is the first presentation of a general solution to this problem in the complex-frequency domain. To achieve this solution a gradient function is calculated and the theory of projection operators is employed. A technique is described by which the optimal open loop control can be implemented in feedback system form.