  This paper presents an explicit solution to decentralized control of a class
of spatially invariant systems. The problem of optimal $H_2$ decentralized
control for cone causal systems is formulated. Using Parseval's identity, the
optimal $H_2$ decentralized control problem is transformed into an infinite
number of model matching problems with a specific structure that can be solved
efficiently. In addition, the closed-form expression (explicit formula) of the
decentralized controller is derived for the first time. In particular, it is
shown that the optimal decentralized controller is given by a specific positive
feedback scheme. A constructive procedure to obtain the state-space
representation of the decentralized controller is provided. A numerical example
is given and compared with previous works which demonstrate the effectiveness
of the proposed method.

Systems and Control