H∞ Model Reduction of Symmetric Systems Using LMIs

In this paper the H_∞ suboptimal model reduction problem for state-space symmetric systems is investigated. Exploiting the state-space symmetric property, there exists some particular solutions of the non-convex constraint sets. An explicit parametrization of all reduced-order models and the solution to the zeroth-order H_∞ approximation problem are obtained using these particular solutions. The infimum of the H_∞ norm between the original and the obtained reduced order model is provided. These results are developed from the linear matrix inequality formulations of the H_∞ control synthesis problem using simple matrix algebraic tools. Numerical examples demonstrate the effectiveness of the theoretical results