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This paper considers the optimal control problem for the general linear time-invariant systems with bounded disturbance,based on the original continuous systems.The optimal control law of a closed-loop system with sampling controller under the quadratic control is concerned.In this case,the relations between sampling step and the stability of systems are discussed,which proves that the upper bound of deviation is ,when the sampling step is not very large.Finally,the ease study illustrates that the relation between sampling step and the stability of the system is only the sufficient condition but not the necessary condition.