Technical Communique: Robust D-stability via positivity

Authors:
D. D. Iljak;D. M. Stipanovi
Affiliations:
Department of Electrical Engineering, Santa Clara University, Santa Clara, CA 95053-0569, USA;Department of Electrical Engineering, Santa Clara University, Santa Clara, CA 95053-0569, USA
Venue:
Automatica (Journal of IFAC)
Year:
1999

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Abstract

The main objective of this paper is to convert the general problem of robust D-stability of a complex polynomial to positivity in the real domain of the corresponding magnitude function. In particular, the obtained criterion for Hurwitz stability is applied to polynomials with interval parameters and polynomic uncertainty structures. The robust stability is verified by testing positivity of a real polynomial using the Bernstein subdivision algorithm. A new feature in this context is the stopping criterion, which is applied whenever the algorithm is inconclusive after a large number of iterations, but we can show that at least one zero of the polynomial is closer to the imaginary axis than a prescribed limit.