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This paper focuses on the problem of designing a decentralized output feedback control strategy for synchronization of homogeneous multi-agent systems with global performance guarantees. The agents under investigation are described as linear singularly perturbed dynamics representing a wide class of physical systems characterized by processes evolving on two time-scales. The collaborative decentralized control is achieved using only output information from neighboring agents and considering that the only available graph information consists in its connectivity, that is, there is no centralized information related to the interconnection network structure. As methodology, the synchronization problem is rewritten as a dynamic output feedback robust stabilization of a singularly perturbed uncertain linear system with guaranteed cost. We show that these problems can be solved by using convex conditions expressed by LMIs and by decoupling the slow and fast dynamics. As an advantage, the fast dynamic matrix can be singular (nonstandard systems) and unstable. The proposed conditions circumvent some drawbacks of the existing works on this topic by providing a dynamic controller that does not depend on the singular parameter or by allowing the design of slow controllers when the fast system is stable. Numerical examples are presented to demonstrate the effectiveness of the proposed protocol and design method.