In this paper, we present an output feedback $H^infty$controller design method and derive the sufficient condition of the bounded real lemma for linear systems with multiple delays in states. For state delayed systems, sufficient conditions for the existence $kappa$-th order $H^infty$controllers are given in terms of three linear matrix inequalities(LMIs). Furthermore, we show how to construct such controllers from the positive definite solutions of their LMIs and given an example to illustrate the validitiy of the proosed design procedure.