First-Order Methods for Solving the Optimal Static ${\cal H}_\infty$-Synthesis Problem

Abstract

In this paper, we consider the static output feedback (SOF) ${\cal H}_\infty$-synthesis problem posed as a nonlinear semi-definite programming (NSDP) problem. Two numerical algorithms are developed to tackle the NSDP problem by solving the corresponding Karush-Kuhn-Tucker first-order necessary optimality conditions iteratively. Numerical results for various benchmark problems illustrating the performance of the proposed methods are given.