Design of Optimally Normal Minimum Gain Controllers by Continuation Method

In this paper, a measure of the departure from normality is investigated for system robustness. An attractive feature of the normality index is in its simplicity for pole placement designs. To allow a tradeoff between system robustness and control effort, a cost function consisting of the sum of a norm of weighted gain matrix and a normality index is minimized. First and second order necessary conditions for the constrained optimization problem is derived and solved by Newton-Raphson algorithm imbedded into a one-parameter family of neighboring zero problems. The method presented in this paper allows the direct computation of optimal gains in terms of robustness and control effort for pole placement problems.