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

This paper presents an explicit solution to decentralized control of a class of spatially invariant systems. The problem of optimal H2 decentralized control for cone causal systems is formulated. Using Parseval’s identity, the optimal H2 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 statespace 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.