Motivated by the sliding mode control methodology, this work presents a stochastic controller design paradigm for linear system with additive Cauchy distributed noises that expands on previous results addressing single-state systems. The control law utilizes the characteristic function of the time propagated probability density function (pdf) of the system state given measurements that has been derived in recent studies addressing the Cauchy estimation problem. The incentive for the proposed approach is mainly the high numerical complexity of the currently available methods for such systems. The controller performance is evaluated numerically and compared to an alternative approach presented recently and to a Gaussian approximation to the problem. A fundamental difference be-tween the Cauchy and the Gaussian controllers is their superior response to noise outliers. The newly proposed Cauchy controller exhibits similar performance to the previously proposed one, while requiring lower computational effort.