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Agent-wise local design methods to synthesize distributed control gains focus on the individual dynamics of each agent to guarantee the overall stability of the system. They are powerful tools due to their scalability. However, the agent-wise local design methods are incapable of maximizing the overall system performance through, for example, decay rate assignment. On the other hand, design methods, which are predicated on a global condition, leads to nonconvex optimization problems. This article considers a global design of an internal model-based distributed dynamic state feedback control law for the linear cooperative output regulation problem. We present a convex formulation of this global design problem based on a structured Lyapunov inequality. Then, the existence of solutions to the structured Lyapunov inequality is investigated. Specifically, we analytically show that the solutions exist for the systems …