Numerical determination of a performance index for improved system response

The paper describes a computer program for the systematic numerical predetermination of a performance index J=¿¿0 (xtQx+u2)dt such that the synthesised feedback controller that minimises J results in a controlled system with satisfactory eigenvalues that all lie to the left of the set {s|s=¿, ¿¿0} in the complex plane. The computer algorithm, which is based on the derivatives of the eigenvalues with respect to the coefficients of Q, may be used in isolation or can be included in an overall synthesis procedure. Examples illustrating the method are included.