Optimal decentralized controllers for spatially invariant systems

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 neighbouring sites. Such a structure arises naturally from spatio-temporal discretizations of many physical systems described by partial differential equations. We consider the problem of optimal design of distributed controllers that have the same information passing delay structure as the plant. We show how the YJBK parametrization of such stabilizing controllers yields a convex parametrization for this class. We then show how the optimal H₂ problem can be solved exactly.