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In this paper, we develop a novel hybrid control framework for addressing consensus problems for multiagent dynamical systems. Specifically, we present hybrid distributed controller architectures for multiagent coordination. The proposed controller architectures are predicated on system thermodynamic notions resulting in thermodynamically consistent hybrid controller architectures involving the exchange of information between agents that guarantee that the closed-loop dynamical network is consistent with basic thermodynamic principles. A unique feature of the proposed framework is that the proposed controller architectures are hybrid and can achieve finite-time coordination. The overall closed-loop dynamics under any of these controller algorithms achieving consensus possesses discontinuous flows since the controller algorithms combine logical switchings with continuous dynamics, leading to impulsive differential equations.