Linear Fractional Representations of Uncertain Systems

We present a new systematic procedure to find low-order linear fractional representations of systems with polynomial parametric uncertainty. The idea is to exploit the structure of the uncertainty to decompose a multidimensional polynomial matrix into sums and products of simple factors for which minimal linear fractional representations can be obtained. This approach is implemented in the structured tree decomposition algorithm, which generates a tree whose leaves are simple factors. An example is presented to illustrate the advantages of this approach.