The cooperative containment control for multiagent systems with high-order linear dynamics under a directed graph is studied. A follower-based observer based on relative outputs of neighboring agents is developed to estimate the relative states of neighbors which avoid designing the observer for the leaders in the existing literature. A matrix transformation is introduced to eliminate the coupling terms resulting from the simultaneous design of observers and controllers. A feasible condition on devising observers and controllers is obtained. Furthermore, the result is extended to deal with the case with transmission time delay. The effectiveness of the proposed design method is verified by providing two simulation examples.