Disturbance attenuation and<tex>H∞</tex>optimization: A design method based on the algebraic Riccati equation

This note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system. The problem under consideration involves attenuating the disturbances to a prespecified level. The construction of the state feedback control law requires the solution of a certain algebraic Riccati equation. By applying the procedure with successively smaller values of the prespecifled disturbance level, the result also provides an approach to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H∞</tex> optimization problem for the state feedback case.