State-space solutions to standard $H_{\infty}$ control problem

Abstract

Simple state-space formulas are derived for all controllers solving a standard $H_{\\infty}$ problem. In this paper, we assume that the systems are finite dimension, continuous-time, linear and time-invariant. There are efficient algorithms to solve Linear Matrix Inequalities. It is enough to reduce the $H_{\\infty}$ problem to a linear matrix inequality by using Riccati inequality.