Stability Conditions for Polytopes of Polynomials

IEEE Transactions on Automatic Control

Volumn 37, Issue 1, 1992, Pages 79-89

  Rantzer, Anders ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--POLYNOMIALS; SYSTEM STABILITY--ANALYSIS;

HURWITZ STABILITY; POLYTOPES; SCHUR STABILITY;

CONTROL SYSTEMS, LINEAR;

EID: 0026679938     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.109640     Document Type: Article

References (11)

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2. A. C. Bartlett, C. V. Hollot, and H. Lin, “Root locations of an entire polytope of polynomials: It suffices to check the edges,” Math. Contr. Signals Syst., vol. 1, pp. 61–71, 1988.
3. H. Chapellat, M. Dahleh, and S. P. Bhattacharyya, “Robust stability under structured and unstructured perturbations,” IEEE Trans. Automat. Contr., vol. 35, pp. 1100–1108, 1990.
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5. V. L. Kharitonov, “Asymptotic stability of an equilibrium position of a family of systems of linear differential equations,” Differential Equations, vol. 14, pp. 1483–1485, 1979.
6. V. L. Kharitonov, “The Routh-Hurwitz problem for families of polynomials and quasi-polynomials,” Izvestiia Akademii nauk Kazakhskoi SSR, Seria fiziko-matematicheskaia, vol. 26, pp. 69–79, 1979.
7. R. J. Minnichelli, J. J. Anagnost, and C. A. Desoer, “An elementary proof of Kharitonov's theorem with extensions,” IEEE Trans. Automat. Contr., vol. 34, pp. 995–998, 1989.
8. I. R. Petersen, “A new extension to Kharitonov's theorem,” in Proc. IEEE Conf. Decision Contr., 1987, pp. 2070-2075.
9. A. Rantzer, “Kharitonov regions and their reciprocals are convex,” Int. J. of Robust and Nonlinear Contr., to be published.
10. A. Rantzer, “Hurwitz testing sets for parallel polytopes of polynomials,” Syst. Contr. Lett., vol. 15, pp. 99–104, 1990.
11. L. A. Zadeh and C. A. Desoer, Linear System Theory. New York: McGraw-Hill, 1963.