A general performance index for analytical design of control systems

A generally applicable performance index for linear feedback systems is proposed. This performance index enables one to specify a desired (ideal) response towards which the system is optimized. The response of any unity-numerator system can be chosen as the ideal response. The coefficients of the performance index are determined from the specified ideal response, and the procedure of optimization is equivalent to minimization of the numerical value of this performance index. The procedure for constructing Liapunov functions for linear systems is used to minimize the performance index. System optimization is illustrated by means of examples. The results indicate that the smaller the numerical value of the performance index, the closer the actual system response approaches the specified ideal response.