Stability margins for Hurwitz polynomials
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The authors treat the robust stability issue using the characteristic polynomial, for two different cases: first in coefficient space with respect to perturbations in the coefficient of the characteristic polynomial; and then for a control system containing perturbed parameters in the transfer function description of the plant. In coefficient space, a simple expression is first given for the l2-stability margin for both the monic and nonmonic cases. Following this, a method is given to find the l-margin, and the method is extended to reveal much larger stability regions. In parameter space the authors consider all single-input (multi-output) or single-output (multi-input) systems with a fixed controller and a plant described by a set of transfer functions which are ratios of polynomials with variable coefficients. A procedure is presented to calculate the radius of the largest stability ball in the space of these variable parameters. The calculation serves as a stability margin for the control system. The formulas that result are quasi-closed-form expressions for the stability margin and are computationally efficient.
Proceedings of the IEEE Conference on Decision and Control
author list (cited authors)
Chapellat, H., Bhattacharyya, S. P., & Keel, L. H.
complete list of authors
Chapellat, H||Bhattacharyya, SP||Keel, LH