This paper considers a synthesis of output regulation controllers which keep the controlled outputs within the prescribed bounds. The controller is designed so that the closed-loop system is equal or similar to the target system with an appropriate input-output relationship. An H_∞ norm is used as an object function to measure a difference between them. The controller is obtained by minimizing the object function via LMI optimization. This paper also provides an LMI-based method for creating the target system which ensures the output regulation.