On structurally constrained H2 performance bounds for stable MIMO plant models

This paper discusses optimal control problems in which the controller must satisfy sparsity structure constraints. Conditions are derived under which the optimal controller associated to an unconstrained quadratic performance index is naturally structured and, as a consequence, the sparsity constraint imposed on the controller has no impact on the optimal loop performance. The results are then applied to study the control of triangular plants that have to be controlled by triangular controllers. We derive explicit characterisations of the Youla parameter that defines an optimal triangular controller and of the performance loss associated to the structural restriction imposed on the controller.