A Fast Algorithm to Compute the Realstructured Stability Radius

We describe a fast algorithm to compute the real structured stability radius with respect to the open left-half plane or the open unit disk. It is based on a recent formula proved by Qiu et al. (Automatica, vol. 31, pp. 879-890, 1995) and the well-known correspondence between the singular values of a transfer function matrix and the imaginary eigenvalues of a related Hamiltonian matrix. Numerical tests suggest that its local convergence is quadratic. 1. Preliminaries. The real structured stability radius measures the ability of a matrix to preserve its \stability" under a certain class of real perturbations. Consider a partitioning of the complex plane C into two disjoint sets C g and C b such that C g is open, i.e., C = C g : C b. A matrix is called C g-stable if its spectrum () is contained in C g. Let us denote the singular values of a p m matrix, ordered is usually abbreviated as r R (A) and called the (unstructured) stability radius of A. Let a transfer function matrix be given through G(s) = C(sI ? A) ?1 B and let @C g denote the boundary of C g. Qiu et al. 2] proved that r ?1 R (A; B; C) = sup s2@C g R G(s) ]; (1) This paper presents research results of the Belgian Programme on Inter-university Poles of Attraction, initiated by the Belgian State, Prime Minister's OOce for Science, Technology and Culture. The scientiic responsibility rests with its authors.