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Abstract
In this paper we propose a non-linear optimization based approach for the computation of the stability region for uncertain polynomials. Both box of polynomials and diamond of polynomials are addressed. Examples are presented as an illustration.
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References
- ANDERSON, B.D., 1972, The reduced Order Hermite Criterion with Applications to Proof of Lienard-Chipart Criterion, IEEE Transaction on Automatic Control, 17:669-672.
- BARMISH, B.O., 1984, Invariance of Strict Hurwitz Property for polynomials with perturbed Coofficients, IEEE Transaction on Automatic Control, 29(10):935-936.
- BARMISH, B.R., TEMPO, R., HOLLOT, C.V. and KANG, H.I, 1992, An Extreme Point Result for Robust Stability of a Diamond of Polynomials, IEEE Transaction on Automatic Control, 37( 9): 1460-1462.
- BLANCHINI, F., TEMPO, R., and DABBCNE, F., 1998, Computation of the Minimum Destabalizing Volume for Interval and Affine Families of Polynomials, IEEE Transaction on Automatic Control, 43(8):1159-1163.
- CHAPELLAT, H., BHATTACHARYYA, S.P., and KEEL, L.H., 1988, Stability Margin for Hurwitz Polynomials, Proceeding of the 27th IEEE Decision and Control Conference, 1:1392-1398.
- DJAFERIS, T.E., 1989, The Largest Stability Hypercube for Families of Polynomials with Lincar Uncertainty, American Control Conference, 1: 633-638.
- HOLLOT, C.V., 1988, On Markov’s Theorem: It is Like Kharitonov’s but Twice as Nice, Proceeding of the 27th IEEE Decision and Control Conference, 1: 515-518.
- KHARITONOV, V.L., 1978,Syumpototic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations Differentsial’nye Uravneniya, 14:2086-2088.
- KIM, K.D., and BOSE, N.K., 1988 Invariance of Strict Hurwitz Property for Bivariate Polynomials Under Coofficients Perturbations, IEEE Transaction on Automatic Control, 33(12):1172-1174.
- MANSOUR, M., and ANDERSON, B.D., 1992, Kharitonov’s Theorem and the Second method of Lyapunov Robustness of Dynamic Systems with Parameter Uncertainties, edited by M. Mansour, Berlin, Birkhauser.
References
ANDERSON, B.D., 1972, The reduced Order Hermite Criterion with Applications to Proof of Lienard-Chipart Criterion, IEEE Transaction on Automatic Control, 17:669-672.
BARMISH, B.O., 1984, Invariance of Strict Hurwitz Property for polynomials with perturbed Coofficients, IEEE Transaction on Automatic Control, 29(10):935-936.
BARMISH, B.R., TEMPO, R., HOLLOT, C.V. and KANG, H.I, 1992, An Extreme Point Result for Robust Stability of a Diamond of Polynomials, IEEE Transaction on Automatic Control, 37( 9): 1460-1462.
BLANCHINI, F., TEMPO, R., and DABBCNE, F., 1998, Computation of the Minimum Destabalizing Volume for Interval and Affine Families of Polynomials, IEEE Transaction on Automatic Control, 43(8):1159-1163.
CHAPELLAT, H., BHATTACHARYYA, S.P., and KEEL, L.H., 1988, Stability Margin for Hurwitz Polynomials, Proceeding of the 27th IEEE Decision and Control Conference, 1:1392-1398.
DJAFERIS, T.E., 1989, The Largest Stability Hypercube for Families of Polynomials with Lincar Uncertainty, American Control Conference, 1: 633-638.
HOLLOT, C.V., 1988, On Markov’s Theorem: It is Like Kharitonov’s but Twice as Nice, Proceeding of the 27th IEEE Decision and Control Conference, 1: 515-518.
KHARITONOV, V.L., 1978,Syumpototic Stability of an Equilibrium Position of a Family of Systems of Linear Differential Equations Differentsial’nye Uravneniya, 14:2086-2088.
KIM, K.D., and BOSE, N.K., 1988 Invariance of Strict Hurwitz Property for Bivariate Polynomials Under Coofficients Perturbations, IEEE Transaction on Automatic Control, 33(12):1172-1174.
MANSOUR, M., and ANDERSON, B.D., 1992, Kharitonov’s Theorem and the Second method of Lyapunov Robustness of Dynamic Systems with Parameter Uncertainties, edited by M. Mansour, Berlin, Birkhauser.