Numerical Algorithm for Model Reduction of Linear Systems with Polytopic Uncertainties

Abstract

In this thesis, we study a H infinity optimal model reduction for polytopic uncertain linearsystem. The polytopic system has its state-space data contained in a convex polytope,a situation that often arises. The problem we are trying to solve is to find alower order polytopic uncertain linear system with a guaranteed H infinity norm error. Asuficient solvability condition is provided in terms of LMIs with one extra couplingrank constraint, which generally leads to a non-convex feasibility problem. To deal with this problem a Cone Complementarity Algorithm with local convergence is used.As an extension a Weighted Model reduction method is proposed for polytopicuncertain linear systems. This method allows us to get a reduced order polytope thatapproximate the original system, for a frequency range that is predefined by inputand output weighting functions. The solvability conditions are also provided in termsof LMIs with an extra coupling rank constraint. The cone complementarity algorithmis used here as well, to deal with the non-convex feasibility problem.