Abstract
In this paper we apply optimization techniques to the problem of robust stability of a family of bivariate polynomials under affine coefficient perturbations. The size of the perturbations is measured by a convex function. In this paper we concentrate onl p weighted norms, for three special casesp = 1,p = 2, andp = ∞. Necessary and sufficient conditions for robust stability are provided. Evaluation of the stability radius is reduced to a minimization problem in two-dimensional space. The results open the door to the development and implementation of reliable and efficient algorithms for the computation of the stability radius.
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Kogan, J. Computation of stability radius for families of bivariate polynomials. Multidim Syst Sign Process 4, 151–165 (1993). https://doi.org/10.1007/BF00986238
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DOI: https://doi.org/10.1007/BF00986238