Optimal ℋ₂ controllers for spatially invariant systems with delayed communication requirements

We consider the problem of optimal ℋ₂ design of semi-decentralized controllers for a special class of spatially distributed systems. This class includes spatially invariant and distributed discrete-time systems with an inherent temporal delay in the interaction of neighboring sites. We consider the problem of optimal design of distributed controllers that have the same information passing delay structure as the plant. We show how for stable plants, the YJBK parameterization of such stabilizing controllers yields a convex parameterization for this class. We then show how the optimal ℋ₂ problem can be solved.