Solution to an inverse problem of locally minimax control and its applications in robust control designs

A given state feedback is shown to be a locally minimax control, satisfying a Bellman-Isaacs inequality associated to a certain linear-quadratic differential game, if and only if the so-called generalized return difference of this feedback satisfies a frequency-domain condition. On this basis, we explore a new approach to robust control designs for nonlinear Lur´e systems with sector bounded uncertainty, linear systems with time-varying norm bounded uncertainty, and multivariable systems with uncertain interconnections, which allows to derive easy to check a frequency-domain test condition for a given state feedback to be the robust controller and does not require to solve matrix equations or inequalities typical for these problems