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Sensitivities of stability constraints and their applications

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1 Author(s)
Biernacki, R. ; Texas A&M University, College Station, TX, USA

Let the real polynomial(a(s) = a_{0} + a_{1}s + ... + a_{n}s^{n}with the coefficients being known differentiable functionsa_{k}(x)be given and let the constraintsg_{i}(x) > 0determine the strictly Hurwitz property of the polynomiala(s). A simple and efficient method to calculate the derivativespartial g_{i}(x)/partial x_{j}is proposed. Then, the application of the method to the problem of stability of polynomials under coefficient perturbation by gradient optimization is discussed. Also, a theorem characterizing the stability region and the newly introduced regions of nondestabilizing perturbations is given.

Published in:

Automatic Control, IEEE Transactions on  (Volume:31 ,  Issue: 7 )

Date of Publication:

Jul 1986

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