Robustness analysis for uncertain dynamical systems with structured perturbations

The authors propose two approaches for robust pole location analysis of dynamical systems with structured parametric uncertainties. The first approach, based on geometric considerations, solves the problem of computing maximal polytopic domains in parameter space for fairly general regions of pole location, when families of polynomials with coefficients affine in the parameters are considered. The solution of the maximal polytope problem also solves the problem of checking root location of a given polytope of polynomials. The second approach, based on algebraic matrix properties, deals with state-space models with structured perturbations. The case in which system matrix entries are perturbed by polynomial functions of physical uncertain parameters is considered. Necessary and sufficient conditions for testing eigenvalue location are given; these conditions are used to derive closed-form solutions of the problem when matrix perturbations depend on one or two uncertain parameters