Weighted optimization theory for nonlinear systems

In this paper, the solution of a nonlinear version of the weighted sensitivity $H^\infty $-optimization problem is discussed. It is shown that the natural object to be considered in this context is a certain “sensitivity operator,” which will be optimized locally in a given “energy ball” (see §5 for the details). In the linear case, the authors are reduced again to the classical sensitivity minimization technique of Zames [21]. The methods were very strongly influenced by the complex analytic power series ideas of [3], [4], [5]. See also the recent results of Ball and Helton [6] for another approach to this subject.