Q-Parametrization and an SDP for H∞-optimal Decentralized Control

We consider the problem of finding decentralized controllers to optimize an H∞-norm. This can be cast as a convex optimization problem when certain conditions are satisfied, but it is an infinite-dimensional problem that still cannot be addressed with existing methods. We use Q-parametrization to approach the original problem with a sequence of finite-dimensional problems. A method is discussed to solve the resulting finite-dimensional approximated convex problem. It is then shown how this problem can be cast as a semidefinite program and generally solved much more efficiently.