On the computation of local quadratic performance indices for hierarchically interconnected systems

In this paper, we present a method to compute approximations of local quadratic performance indices for hierarchically interconnected LTI subsystems with a global performance index. The presented method builds on previous work on a decomposition scheme for the design of distributed controllers with optimized
H
₂
-performance and network topology. This decomposition method relies on the computation of local quadratic performance indices for each subsystem that reflect the change of the global performance for a change of the local controller parametrization. In the work on hand, we use ideas from moment-matching and least norm problems to obtain approximative local performance indices.