Factorization and smallest-norm roots of multivariable polynomials in robustness analysis

Robustness analysis for linear time invariant (LTI) systems subject to parametric uncertainty is formulated in terms of the smallest-norm root of a multivariable polynomial. An algorithm is devised for factorization into smaller-degree polynomials. The authors then characterize, with a convex optimization algorithm, a generic class of systems for which the largest stability hypercube touches the stability boundary on a corner. The whole method enables reduction and simplification of the analysis problem. A flexible plant example illustrates the results