Reactive systems respond to internal or external stimuli and act in an event-driven manner. It is generally difficult to specify a complex reactive systems behavior. One reason is that actual reactive systems are usually formed by combining plural sequential machines that behave concurrently. This paper presents the state diagram matrix (SDM) which is a visual and hierarchical formalism of a reactive system's behavior. SDM involves two concepts. The first is a matrix plane description, on which a 3-dimensional state space is projected. The second is state composition and state abstraction for hierarchical sequential machine definition. The Petri net model is used for the composition of parallel sequential machines. The understandability and reliability of control software is shown to be improved as a consequence of adopting SDM for specifying disk-subsystem control requirements. The development support functions of SDM using a workstation are also described.