Numerical algorithm for model reduction of polytopic uncertain linear systems

In this paper we study a numerical algorithm for model reduction problem of polytopic uncertain linear systems. 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 a lower order polytopic uncertain linear system with a guaranteed induced L₂ norm error. A sufficient solvability condition was provided in terms of LMIs with one extra coupling rank constraint, which generally leads to a non-convex feasibility problem. To deal with this problem, a cone complementarity algorithm is developed, although only local convergence is guaranteed.