Optimization of linear multivariable systems with prespecified closed-loop eigenvalues

The optimal control of linear time-invariant systems, with respect to a given quarature performance criterion, is investigated when the closed-loop eigenvalues are prespecified. The performance criterion is averaged to eliminate its dependence on the initial states. Then, expressions are given for the gradient of the cost with respect to the parameters of the class of controllers that satisfy the closed-loop eigenvalues requirement. In addition, an algorithm for computing the optimal controller is presented and a numerical example is worked out to demonstrate the feasibility of the proposed algorithm.