DOI: 10.1007/bf02551236. Root locations of an entire polytope of polynomials: It suffices to check the edges

Root locations of an entire polytope of polynomials: It suffices to check the edges

10.1007/bf02551236

Crossref journal-article

Springer Science and Business Media LLC

Mathematics of Control, Signals, and Systems (297)

Bibliography

Bartlett, A. C., Hollot, C. V., & Lin, H. (1988). Root locations of an entire polytope of polynomials: It suffices to check the edges. Mathematics of Control, Signals, and Systems, 1(1), 61â71.

Authors 3

A. C. Bartlett (first)
C. V. Hollot (additional)
Huang Lin (additional)

References 18 Referenced 384

[A1] J. Ackermann, Parameter space design of robust control systems,IEEE Trans. Automat. Control,25 (1980), 1058–1072. (10.1109/TAC.1980.1102505) / IEEE Trans. Automat. Control by J. Ackermann (1980)
J. Ackermann, Design of robust controllers by multi-model methods,Proceedings of the Seventh International Symposium on Mathematical Theory of Networks and Systems, Stockholm, 1985.
[B1] B. R. Barmish, Invariance of the strict Hurwitz property for polynomials with perturbed coefficients,IEEE Trans. Automat. Control,29 (1984), 935–936. (10.1109/TAC.1984.1103401) / IEEE Trans. Automat. Control by B. R. Barmish (1984)
[BG] S. Bialas and J. Garloff, Convex combinations of stable polynomials,J. Franklin Inst.,319 (1985), 373–377. (10.1016/0016-0032(85)90057-2) / J. Franklin Inst. by S. Bialas (1985)
[B2] N. K. Bose, A system-theoretic approach to stability of sets of polynomials,Contemp. Math.,47 (1985), 25–34. (10.1090/conm/047/828290) / Contemp. Math. by N. K. Bose (1985)
[C] P. L. Chebyshev,Complete Collected Works, Vol. 3. pp. 307–362, Izd. AN SSSR, Moscow, 1948. / Complete Collected Works by P. L. Chebyshev (1948)
[FM] A. T. Fam and J. S. Meditch, A canonical parameter space for linear system design,IEEE Trans. Automat. Control,23 (1978), 454–458. (10.1109/TAC.1978.1101744) / IEEE Trans. Automat. Control by A. T. Fam (1978)
[G1] F. R. Gantmacher,The Theory of Matrices, Chelsea, New York, 1960. / The Theory of Matrices by F. R. Gantmacher (1960)
[G2] B. K. Ghosh, Some new results on the simultaneous stabilizability of a family of single input, single output systems,Systems Control Lett.,6 (1985), 39–45. (10.1016/0167-6911(85)90052-0) / Systems Control Lett. by B. K. Ghosh (1985)
[HB] C. V. Hollot and A. C. Bartlett, Some discrete-time counterparts to Kharitonov's stability criterion for uncertain systems,IEEE Trans. Automat. Control,31 (1986), 355–356. (10.1109/TAC.1986.1104268) / IEEE Trans. Automat. Control by C. V. Hollot (1986)
[HHB] L. Huang, C. V. Hollot, and A. C. Bartlett, Stability of families of polynomials: considerations in coefficient space,Internat. J. Control,45 (1987), 649–660. (10.1080/00207178708933757) / Internat. J. Control by L. Huang (1987)
[K] V. L. Kharitonov, Asymptotic stability of an equilibrium position of a family of systems of linear differential equations,Differentsial'nye Uravneniya,14 (1978), 2086–2088. / Differentsial'nye Uravneniya by V. L. Kharitonov (1978)
[M] A. A. Markov,Collected Works, pp. 78–105, Nauka, Moscow, 1948. / Collected Works by A. A. Markov (1948)
[N] Y. I. Naimark,Stability of Linearized Systems, Leningrad Aeronautical Engineering Academy, Leningrad, 1949. / Stability of Linearized Systems by Y. I. Naimark (1949)
[R] R. T. Rockafellar,Convex Analysis, Princeton University Press, Princeton, 1972. / Convex Analysis by R. T. Rockafellar (1972)
[S] D. D. Siljak,Nonlinear Systems, The Parameter Analysis and Design, Wiley, New York, 1969. / Nonlinear Systems, The Parameter Analysis and Design by D. D. Siljak (1969)
[SBD] C. B. Soh, C. S. Berger, and K. P. Dabke, On the stability of polynomials with perturbed coefficients,IEEE Trans. Automat. Control,30 (1985), 1033–1036. (10.1109/TAC.1985.1103807) / IEEE Trans. Automat. Control by C. B. Soh (1985)
K. H. Wei and B. R. Barmish, On making a polynomial Hurwitz invariant by choice of feedback gains,Proceedings of the 24th IEEE Conference on Decision and Control, Fort Lauderdale, FL, 1985. (10.1109/CDC.1985.268581)

Dates

Type	When
Created	18 years, 7 months ago (Jan. 5, 2007, 6:34 a.m.)
Deposited	6 years, 3 months ago (May 19, 2019, 5:50 p.m.)
Indexed	7 minutes ago (Aug. 30, 2025, 4:58 p.m.)
Issued	37 years, 6 months ago (Feb. 1, 1988)
Published	37 years, 6 months ago (Feb. 1, 1988)
Published Print	37 years, 6 months ago (Feb. 1, 1988)

Funders 0

None

BibTeX

@article{Bartlett_1988, title={Root locations of an entire polytope of polynomials: It suffices to check the edges}, volume={1}, ISSN={1435-568X}, url={http://dx.doi.org/10.1007/bf02551236}, DOI={10.1007/bf02551236}, number={1}, journal={Mathematics of Control, Signals, and Systems}, publisher={Springer Science and Business Media LLC}, author={Bartlett, A. C. and Hollot, C. V. and Lin, Huang}, year={1988}, month=feb, pages={61–71} }

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