| Structured control has been the object of interest in recent years, especially for the interconnected networks. This technique allows for the control law to respect specific structures, such as topological or interconnection structure. This dissertation deals with the structured model reduction problem and the structured H2 control problem for large-scale interconnected systems; we would like the resulting reduced system or controller to admit the corresponding structures (decentralized, localized, specific, or arbitrary structures). We show that if we relax the algebraic Riccati equations to inequalities and force the solution to be decentralized, the addressed problems become convex.; Balanced truncation and two of its extended variants, normalized coprime factor and frequency weighted model reduction are briefly reviewed. Structured coprime factor model reduction, which includes expansive and contractive co-prime factor methods, is extensively studied and a proof of stability is provided for the contractive case.; We extend the structured coprime factor model reduction to the frequency weighted problems to have the model accuracy vary with frequency. It turns out that the feasibility of resulting LMI method can be greatly enhanced through frequency weighting.; In the structured H2 control problem, a direct relationship between the Linear Matrix Inequality approach of Scherer and the classic Algebraic Riccati Equation approach is provided. Based on this observation, a set of suboptimal structured controllers are derived, and a bound on every controller's performance is also obtained. |
