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This paper studies a stabilization problem for linear MIMO systems subject toexternal perturbation that further requires the closed-loop system render aspecified gain from the external perturbation to the output. The problem arisesfrom control of networked systems, in particular, robust output synchronizationof heterogeneous linear MIMO multi-agent systems via outputfeedback/communication. We propose a new approach that converts a class of MIMOsystems into a normal form via repeated singular value decomposition and provethat a stabilization controller with a specified external gain can beexplicitly constructed for the normal form.Two scenarios with static statefeedback and dynamic output feedback are investigated. By integrating thereference model and internal model techniques, the robust outputsynchronization problem for MIMO multi-agent systems is converted into astabilization problem with a specified externalgain and solved by the developedapproach.

Stabilization with a Specified External Gain for Linear MIMO Systems and Its Applications to Control of Networked Systems