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Robust stability of a class of positive quasi-polynomials in Banach spaces. (English. Russian original) Zbl 1229.93125

Math. Notes 88, No. 5, 626-636 (2010); translation from Mat. Zametki 88, No. 5, 651-661 (2010).
Summary: We study the stability radii of positive quasipolynomials associated with linear functional difference equations in infinite-dimensional spaces. It is shown that the positive, real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by a simple example.

MSC:

93D09 Robust stability
93C73 Perturbations in control/observation systems
93C05 Linear systems in control theory
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