A new method of evaluating quadratic and time-weighted quadratic form performance indices

A new method of evaluating quadratic form performance indices, time and time- squared-weighted quadratic form performance indices for a linear time-invariant regulator system described by state variable equations X = AX is presented in this paper. The performance indices are evaluated completely in time domain, and hence the method requires no knowledge of either the Laplace transform or the complex variable theory. It is brought out that this method is much simpler than the methods available in. the literature. A numerical example for a third-order system is worked out to illustrate the method. The performance indices ISE, 1TSE and ISTSE (for type-1 unity feedback systems) that are extensively used and reported in the literature are obtained in this paper as a special case of the method used here for evaluating the more general quadratic form performance indices. © 1971 Taylor & Francis Group, LLC.