On the design of optimal regulators using time-multiplied performance index with prescribed closed-loop eigenvalues

In this paper, an algorithm is developed to compute an optimal constant state feedback in a linear multivariable system yielding prescribed closed-loop eigenvalues and minimizing, in an average sense, a given time-multiplied quadratic performance index. An example is worked out to reveal the contradiction of the conclusions in [1]-[3] concerning the effect of that performance index on the transient response of the control system.