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This paper presents an explicit solution to decentralized control of a classof spatially invariant systems. The problem of optimal $H_2$ decentralizedcontrol for cone causal systems is formulated. Using Parseval's identity, theoptimal $H_2$ decentralized control problem is transformed into an infinitenumber of model matching problems with a specific structure that can be solvedefficiently. In addition, the closed-form expression (explicit formula) of thedecentralized controller is derived for the first time. In particular, it isshown that the optimal decentralized controller is given by a specific positivefeedback scheme. A constructive procedure to obtain the state-spacerepresentation of the decentralized controller is provided. A numerical exampleis given and compared with previous works which demonstrate the effectivenessof the proposed method.

Optimal $H_2$ Decentralized Control of Cone Causal Spatially Invariant Systems