  The H2 guaranteed cost decentralized control problem is investigated in this
work. More specifically, on the basis of an appropriate H2 re-formulation that
we put in place, the optimal control problem in the presence of parameter
uncertainties is then suitably characterized by convex restriction and solved
in parameter space. It is shown that a set of stabilizing decentralized
controller gains for the uncertain system is parameterized in a convex set
through appropriate convex restriction, and then an approximated conic
optimization problem is constructed. This facilitates the use of the symmetric
Gauss-Seidel (sGS) semi-proximal augmented Lagrangian method (ALM), which
attains high computational effectiveness. A comprehensive analysis is given on
the application of the approach in solving the optimal decentralized control
problem; and subsequently, the preserved decentralized structure, robust
stability, and robust performance are all suitably guaranteed with the proposed
methodology. Furthermore, an illustrative example is presented to demonstrate
the effectiveness of the proposed optimization approach.
