In this paper, a new class of composite systems, called switched composite systems, whose subsystems are switched systems is proposed. This class of systems can be viewed as a natural extension of both composite systems and switched systems. We design decentralized switching laws for this class of systems to be asymptotically stable. For general composite systems, decentralized hybrid state feedback and output feedback are introduced. All results are given by linear matrix inequalities (LMIs), which are easier to realize.