2017/02/08 by Nicola Guglielmi, Guglielmi, Nicola, Mert Gürbüzbalaban +6
Computer Science · Engineering · #Control Systems and Identification #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.1702.02486
openalex publication_date 2017/02/08 · openalex created_date 2022/09/26 · openalex updated_date 2026/07/28
We propose a fast method to approximate the real stability radius of a linear\ndynamical system with output feedback, where the perturbations are restricted\nto be real valued and bounded with respect to the Frobenius norm. Our work\nbuilds on a number of scalable algorithms that have been proposed in recent\nyears, ranging from methods that approximate the complex or real pseudospectral\nabscissa and radius of large sparse matrices (and generalizations of these\nmethods for pseudospectra to spectral value sets) to algorithms for\napproximating the complex stability radius (the reciprocal of the H_\∞\nnorm). Although our algorithm is guaranteed to find only upper bounds to the\nreal stability radius, it seems quite effective in practice. As far as we know,\nthis is the first algorithm that addresses the Frobenius-norm version of this\nproblem. Because the cost mainly consists of computing the eigenvalue with\nmaximal real part for continuous-time systems (or modulus for discrete-time\nsystems) of a sequence of matrices, our algorithm remains very efficient for\nlarge-scale systems provided that the system matrices are sparse.\n