Model reduction with guaranteed stability

Convex parameterization of stability domain in coefficient space has received much attention recently. Currently most advanced, LMI, parameterization lacks the way to determine its free parameter, the ¿central polynomial¿, in a good way. Recent papers proposed some better candidate for central polynomial compared to the original method. In this note we consider an application of convex parameterization of stability domain to ensure stability of polynomial during model reduction process. The main novelty of the note is in the way we choose the central polynomial and in the way we solve a linear semi-infinite programming problem with LMI constraints. We propose an iterative procedure to choose better central polynomial at each iteration, relaxing the stability constraints imposed on model reduction process in each iteration. Example is provided illustrating the effectiveness of the proposed procedure.