H2 order and parameter dependency reduction of uncertain linear systems using LMI relaxations

This article presents a new approach for model reduction of continuous-time uncertain linear systems using the H2norm as performance criterion. Two main novelties are proposed when compared to previous approaches from the literature. The first one is the possibility of removing a subset of the uncertain parameters, potentially resulting in a simpler model with a small approximation error with respect to the original model. The second is concerned with the linearization of the classic non-convex inequalities associated to order reduction, helping to improve the synthesis procedure in terms of less conservative approximation errors. The design conditions are provided in terms of LMI relaxations associated to scalar searches and iterative procedures. Numerical examples from the literature are used to illustrate the potentialities of the proposed approach when compared to existing methods.