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Epilogue

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Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 201)

Keywords

State Feedback Linear Matrix Inequality Lyapunov Stability Lyapunov Stability Theory Constrain Minimization Problem 
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Bibliography

  1. [A]
    Ackermann J., Does it suffice to check a subset of multilinear parameters in robustness analysis? IEEE Trans. Autom. Contr., Vol. AC-37, No. 4, pp. 487–488, 1992.Google Scholar
  2. [AB]
    Agathoklis P., Bruton L., Practical-BIBO stability of n-dimensional discrete systems. IEE Proceedings, Vol. 130, Pt. G, No. 6, pp. 236–242, 1983.Google Scholar
  3. [AG]
    Adams W.W., Goldstein L.J., Introduction to Number Theory. Prentice Hall, New Jersey, 1976.Google Scholar
  4. [AH]
    Avellar C.E., Hale J.K., On the zeros of exponential polynomials. Journal of Mathematical Analysis and Applications, Vol. 73, pp. 434–452, 1980.Google Scholar
  5. [AHK]
    Ackermann J., Hu H.Z., Kaesbauer D., Robustness analysis: a case study. IEEE Trans. Autom. Contr., Vol. AC-35, No. 3, pp. 352–356, 1990.Google Scholar
  6. [ADM]
    Anagnost J.J., Desoer C.A., Minnichelli R.J., Generalized Nyquist tests for robust stability: frequency domain generalizations of Kharitonov's theorem, pp. 79–96 in Robustness in Identification and Control, Milanese M., Tempo R., Vicino A., (eds.) International Workshop on Robustness in Identification and Control, Turin, Italy 1988. Plenum Press, 1989.Google Scholar
  7. [AJM]
    Anderson B.D.O., Jury E.I., Mansour M., On robust Hurwitz polynomials. IEEE Trans. Autom. Contr. Vol. AC-32, No. 10, pp. 909–913, 1987.Google Scholar
  8. [AKMD]
    Anderson B.D.O., Kraus F., Mansour M., Dasgupta S., Easily testable sufficient conditions for the robust stability of systems with multilinear parameter dependence, pp. 81–92 in Robustness of Dynamic Systems with Parameter Uncertainties. Mansour M., Balemi S., Truol W., (editors). Monte Verità, Birkhäuser Verlag Basel, 1992.Google Scholar
  9. [Bar]
    Barmish B.R., New Tools for Robustness of Linear Systems. Macmillan, New York, 1994.Google Scholar
  10. [Bart]
    Bartlett A.C., Counter-example to “Clockwise nature of Nyquist locus of stable transfer functions”. Int. J. Contr., Vol. 51, No. 6, pp. 1479–1483, 1990.Google Scholar
  11. [Bas]
    Basu S., On the multidimensional generalization of robustness of scattering Hurwitz property of complex polynomials. IEEE Trans. on Circuits and Systems, Vol. 36, No. 9, pp. 1159–1167, 1989.Google Scholar
  12. [Ber]
    Berge C., Topological Spaces. Macmillan, New York, 1963.Google Scholar
  13. [Blo]
    Blondel V., Simultaneous Stabilization of Linear Systems. Lecture Notes in Control and Information Sciences, Volume 191, Springer-Verlag, London, 1994.Google Scholar
  14. [Boel]
    Boese F.G., Stability in a special class of retarded difference-differential equations with interval-valued coefficients. Journal of Mathematical Analysis and Applications, Vol. 181, pp. 227–247, 1994.Google Scholar
  15. [Boe2]
    Boese F.G., On the stability of real exponential polynomials with interval-valued delays. Multidimensional Systems and Signal Processing, in press.Google Scholar
  16. [Bos1]
    Bose N.K., Problems and progress in multidimensional systems theory. Proceedings of the IEEE, Vol. 65, No. 6, pp. 824–840, 1977.Google Scholar
  17. [Bos2]
    Bose N.K., Applied Multidimensional Systems Theory. Van Nostrand Reinhold, 1982.Google Scholar
  18. [Bos3]
    Bose N.K., Boundary Implication Results in Parameter Space, pp. 47–57 in Handbook of Statistics, Vol. 10. Bose N.K., Rao C.R. (eds.), Elsevier Science Publishers, 1993.Google Scholar
  19. [Bos4]
    Bose N.K., Inference of Properties of Sets from Subsets, Chapter 4 in Multivariate Analysis: Futire Directions. Rao C.R. (ed.), Elsevier Science Publishers, 1993.Google Scholar
  20. [Bru]
    Brumley W.E., On the asymptotic behavior of solutions of differential-difference equations of neutral type. Journal of Differential Equations, Vol. 7, pp. 175–188, 1970.Google Scholar
  21. [BB]
    Boyd S.P., Barratt C.H., Linear Controller Design. Prentice Hall, New Jersey, 1991.Google Scholar
  22. [BC]
    Bellman R., Cooke K.L., Differential-Difference Equations. Academic Press, New York, 1963.Google Scholar
  23. [BhK]
    Bhattacharyya S.P., Keel L.H., Robust stability and control of linear and multilinear interval systems, pp. 31–77 in Robust Control Systems, Techniques and Applications. Control and Dynamic Systems, Vol. 51, Part 2, Leondes C.T. (ed.). Academic Press, 1992.Google Scholar
  24. [BoK]
    Bose N.K., Kim K.D., Stability of a complex polynomial set with coefficients in a diamond and generalizations. IEEE Trans. on Circuits and Systems, Vol. 36, No. 9, pp. 1168–1174, 1989.Google Scholar
  25. [BP]
    Barmish B.R., Polyak B.T., The volumetric singular value and robustness of feedback control systems. Technical Report ECE-93-9, Department of Electrical and Computer Engineering, University of Wisconsin-Madison, 1993.Google Scholar
  26. [BS1]
    Barmish B.R., Shi Z., Robust stability of a class of polynomials with coefficients depending multilinearly on perturbations. IEEE Trans. Autom. Contr., Vol. AC-35, No. 9, pp. 1040–1043, 1990.Google Scholar
  27. [BS2]
    Barmish B.R., Shi Z., Robust stability of perturbed systems with time delays. Automatica, Vol. 25, No. 3, 1989, pp. 371–381.Google Scholar
  28. [BG]
    Blondel V., Gevers M., The simultaneous stabilizability of three linear systems is rationally undecidable. Math. Contr., Signals Syst., Vol. 6, pp. 135–145, 1994.Google Scholar
  29. [BZ]
    Bose N.K., Zeheb E., Kharitonov's theorem and stability test for multidimensional digital filters. IEE Proc.-G, Vol. 133, No. 4, pp. 187–190, 1986.Google Scholar
  30. [BAH]
    Barmish B.R., Ackermann J., Hu H., The tree structured decomposition: A new approach to robust stability analysis. Proceedings of the Conference on Information Sciencies and Systems. Princeton, New Jersy, pp. 133–145, 1990.Google Scholar
  31. [BHH]
    Bartlett A.C., Hollot C.V., Huang L., Root locations of an entire polytope of polynomials: It suffices to check the edges. Math. Contr., Signals Syst., Vol. 1, pp. 61–71, 1988.Google Scholar
  32. [BBFE]
    Boyd S., Balakrishnan V., Feron E., El Ghaoui L., Control system analysis and synthesis via linear matrix inequalities. Proceedings of the 1993 ACC, San Francisco, California, pp. 2200–2206, 1993.Google Scholar
  33. [BEFB]
    Boyd S., El Ghaoui L., Feron E., Balakrishnan V., Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Applied Mathematics, Vol. 15, 1994.Google Scholar
  34. [BHKT]
    Barmish B.R., Hollot C.V., Kraus F.J., Tempo R., Extreme point results for robust stabilization of interval plants with first order compensators. IEEE Trans. Autom. Contr., Vol. AC-37, No. 6, pp. 707–714, 1992.Google Scholar
  35. [BTHK]
    Barmish B.R., Tempo R., Hollot C.V., Kang H.I., An extreme point result for robust stability of a diamond of polynomials. Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, pp. 37–38, 1990.Google Scholar
  36. [CB]
    Chapellat H., Bhattacharyya S.P., A generalization of Kharitonov's theorem: robust stability of interval plants. IEEE Trans. Autom. Contr., Vol. AC-34, No. 3, pp. 306–311, 1989.Google Scholar
  37. [CM]
    Chui C.K., Mhaskar H.N., On multivariate robust stability. SIAM J. Control and Optimization, Vol. 30, No. 5, pp. 1190–1199, 1992.Google Scholar
  38. [CK1]
    Cohen N., Kogan J., Convexity of a frequency response arc associated with a stable entire function. Mathematics Research Report KOG 94-03, Department of Mathematics, University of Maryland Baltimore County.Google Scholar
  39. [CK2]
    Cohen N., Kogan J., Convexity of a frequency response arc associated with a stable quasipolynomial. Mathematics Research Report KOG 94-02, Department of Mathematics, University of Maryland Baltimore County.Google Scholar
  40. [CBD]
    Chapellat H., Bhattacharyya S.P., Dahleh M., Robust stability of a family of disc polynomials. Int. J. Contr., Vol. 51, pp. 1353–1362, 1990.Google Scholar
  41. [CBL]
    Chiasson J., Brierley S.D., Lee E.B., A simplified derivation of the Zeheb-Walach 2-D stability test with applications to time-delay systems. IEEE Trans. Autom. Contr., Vol. AC-30, No. 4, pp. 411–414, 1985.Google Scholar
  42. [CFN]
    Chen J., Fan M.K.H., Nett C.N., On μ and stability of uncertain polynomials. Proceedings of the 1990 ACC, pp. 2200–2206.Google Scholar
  43. [CKB]
    Chapellat H., Keel L.H., Bhattacharyya S.P., Robustness properties of multilinear interval systems, pp. 73–80 in Robustness of Dynamic Systems with Parameter Uncertainties. Mansour M., Balemi S., Truol W., (editors). Monte Verità, Birkhäuser Verlag Basel, 1992.Google Scholar
  44. [D]
    Doyle J., Analysis of feedback systems with structured uncertainties. IEE Proceedings, Vol. 129, Part D, pp. 242–250, 1982.Google Scholar
  45. [DH]
    Djaferis T.E., Hollot C.V., Parameter partitioning via shaping condition for the stability of families of polynomials. IEEE Trans. Autom. Contr., Vol. AC-34, No. 11, pp. 1205–1209, 1989.Google Scholar
  46. [DS]
    De Gaston R.R.E., Safonov M.G., Exact calculation of the multiloop stability margin. IEEE Trans. Autom. Contr., Vol. AC-33, No. 2, pp. 156–171, 1988.Google Scholar
  47. [DCC]
    Desages A.C., Castro L., Cendra H., Distance of a complex coefficient stable polynomial from the boundary of the stability set. Multidimensional Systems and Signal Processing, Vol. 2, pp. 189–210, 1991.Google Scholar
  48. [FD]
    Frazer R.A., Duncan W.J., On the criteria for stability for small motions. Proceedings of the Royal Society A, Vol. 124, pp. 642–654, 1929.Google Scholar
  49. [FS1]
    Foo Y.K., Soh Y.C., Root clustering of interval polynomials in the left-sector. Systems and Control Letters, Vol. 13, pp. 239–245, 1989.Google Scholar
  50. [FS2]
    Foo Y.K., Soh Y.C., Stability of a family of polynomials with coefficients bounded in a diamond. IEEE Transactions on Automatic Control, Vol. AC-36, No. 12, pp. 1501–1502, 1991.Google Scholar
  51. [FDB]
    Fu M., Dasgupta S., Blondel V., Robust stability under a class of nonlinear parametric perturbations. Preprint, 1992.Google Scholar
  52. [FOP1]
    Fu M., Olbrot A.W., Polis M.P., Robust stability for time-delay systems: the edge theorem and graphical tests. IEEE Transactions on Automatic Control, Vol. 34, No. 8, pp. 813–820, 1989.Google Scholar
  53. [FOP2]
    Fu M., Olbrot A.W., Polis M.P., The Edge theorem and graphical tests for robust stability of neutral time-delay systems. Automatica, Vol. 27, No. 4, pp. 739–741, 1991.Google Scholar
  54. [Ga]
    Gantmacher F.R., The Theory of Matrices, Chelsea, New York, 1964.Google Scholar
  55. [Go1]
    Goodman D., Some stability properties of two-dimensional linear shift-invariant digital filters. IEEE Trans. Circuits Syst., Vol. CAS-24, No. 4, pp. 201–207, 1977.Google Scholar
  56. [Go2]
    Goodman D., Some difficulties with the double bilinear transformation in 2-D recursive filter design. Proceedings of the IEEE, Vol. 66, No. 7, pp. 796–797, 1978.Google Scholar
  57. [H]
    Horowitz I., Survey of quantitative feedback theory (QFT). Int. J. Contr., Vol. 53, pp. 255–291, 1991.Google Scholar
  58. [HaB]
    Hamann J.C., Barmish B.R., Convexity of frequency response arcs associated with a stable polynomial. IEEE Trans. Autom. Contr. Vol. AC-38, No. 6, pp. 904–915, 1993.Google Scholar
  59. [HP1]
    Hinrichsen D., Pritchard A.J., Stability radius for structured perturbations and the algebraic Riccati equation. Systems and Control Letters, Vol. 8, pp. 105–113, 1986.Google Scholar
  60. [HP2]
    Hinrichsen D., Pritchard A.J., Real and complex stability radii: a survey. pp. 119–162 in Control of Uncertain Systems, D. Hinrichsen, A.J. Pritchard eds., Proceedings of an International Workshop, Bremen, West Germany, June 1989. Boston, Birkhauser, 1990.Google Scholar
  61. [HP3]
    Hinrichsen D., Pritchard A.J., Robustness measures for linear systems with application to stabilit radii of Hurwitz and Schur polynomials. Int. J. Contr., Vol. 55, No. 4, pp. 809–844, 1992.Google Scholar
  62. [HS]
    Holohan A.M., Safonov M.G., Some counterexamples in robust stability theory. Systems and Control Letters, Vol. 21, pp. 95–102, 1993.Google Scholar
  63. [HX]
    Hollot C.V., Xu Z.L., When the image of a multilinear function is a polytope? A conjecture. Proceedings of the 28th IEEE Conference on Decision and Control, Tampa, Florida, pp. 1890–1891, 1989.Google Scholar
  64. [HoB]
    Horisberger H.P., Bélanger P.R., Regulators for linear, time invariant plants with uncertain parameters. IEEE Trans. Autom. Contr., Vol. AC-21, No. 5, pp. 705–708, 1976.Google Scholar
  65. [HBA]
    Horowitz I., Ben-Adam S., Clockwise nature of Nyquist locus of stable transfer function. Int. J. Contr., Vol. 49, pp. 1433–1436, 1989.Google Scholar
  66. [HIT]
    Hale J.K., Infante E.F., Tsen F.-S.P., Stability in linear delay equations. Journal of Mathematical Analysis and Applications, Vol. 105, pp. 533–555, 1985.Google Scholar
  67. [HKZ1]
    Hocherman J., Kogan J., Zeheb E., Simple stability criterion for quasipolynomial families with uncertain coefficients and uncertain delays. Proceedings of the 32th IEEE Conference on Decision and Control, San Antonio, Texas, 1993.Google Scholar
  68. [HKZ2]
    Hocherman J., Kogan J., Zeheb E., On exponential stability of linear systems and Hurwitz stability of characteristic quasipolynomials. EE Publication No. 892, Department of Electrical Engineering, Technion-Israel Institute of Technology, 1993.Google Scholar
  69. [HKKZ]
    Hocherman J., Kharitonov V.L., Kogan J., Zeheb E., On the stability of quasipolynomials with weighted diamond coefficients. Multidimensional Systems and Signal Processing, in press.Google Scholar
  70. [J1]
    Jury E.I., Stability of multidimensional scalar and matrix polynomials. Proceedings of the IEEE, Vol. 66, No. 9, pp. 1018–1047, 1978.Google Scholar
  71. [J2]
    Jury E.I., Inners and Stability of Dynamic Systems. Wiley, New York, 1974.Google Scholar
  72. [J3]
    Jury E.I., Stability of multidimensional systems and related problems. Chapter 3 in Multidimensional Systems: Techniques and Applications. S.G. Tzafestas (ed.), Marcel Dekker, New York, 1985.Google Scholar
  73. [JB]
    Jury E.I., Bauer P., On the stability of two-dimensional continuous systems. IEEE Trans. on Circuits and Systems, Vol. 35, No. 12, pp. 1487–1500, 1988.Google Scholar
  74. [Kah]
    Kahan W., Numerical linear algebra. Canadian Math. Bull., Vol. 9, pp. 756–801, 1966.Google Scholar
  75. [Kai]
    Kailath, T., Linear Systems. Prentice-Hall, Englewood Cliffs, N.J., 1980.Google Scholar
  76. [Kam]
    Kamen E.W., On the relation between zero criteria for two variable polynomials and asymptotic stability of delay differential equations. IEEE Trans. Autom. Contr., Vol. AC-25, No. 5, pp. 983–984, 1980.Google Scholar
  77. [Kh]
    Kharitonov V.L., Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differential Equations, Vol. 14, pp. 1483–1485, 1979.Google Scholar
  78. [Ko1]
    Kogan J., Computation of stability radius for families of bivariate polynomials. Multidimensional Systems and Signal Processing, Vol. 4, 1993, pp. 151–165.Google Scholar
  79. [Ko2]
    Kogan J., Stability of a polynomial and convexity of a frequency response arc. Proceedings of the 32th IEEE Conference on Decision and Control, San Antonio, Texas, 1993.Google Scholar
  80. [KJ1]
    Katbab A., Jury E.I., Robust Schur stability of a complex coefficient polynomial set with coefficients in a diamond. Journal of the Franklin Institute, Vol. 327, No. 5, pp. 687–698, 1990.Google Scholar
  81. [KJ2]
    Katbab A., Jury E.I., Generalization and comparison of two recent frequency-domain stability robustness results. Int. J. Contr., Vol. 53, No. 2, pp. 463–475, 1991.Google Scholar
  82. [KL1]
    Kogan J., Leizarowitz A., Frequency domain criterion for robust stability of interval time-delay systems. Automatica, in press.Google Scholar
  83. [KL2]
    Kogan J., Leizarowitz A., Exponential stability of linear systems with commensurate time-delays. Mathematics Research Report, March 28, 1994. Department of Mathematics, University of Maryland Baltimore County.Google Scholar
  84. [KM]
    Kraus F.J., Mansour M., On robust stability of discrete systems. Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, Hawaii, pp. 421–422, 1990.Google Scholar
  85. [KP]
    Kiselev O.N., Polyak B.T., Robust gain margin for a cascade of uncertain links. Preprint, 1994.Google Scholar
  86. [KT]
    Kharitonov V.L., Tempo R., On stability of a weighted diamond of real polynomials CENS-CNR Technical Report 11, 1992.Google Scholar
  87. [KZ]
    Kharitonov V.L., Zhabko A.P., Robust stability of time-delay systems. IEEE Trans. Autom. Contr., in press.Google Scholar
  88. [KAM]
    Kraus F.J., Anderson B.D.O., Mansour M., Robust stability of polynomials with multilinear parameter dependence. Int. J. Contr., Vol. 50, No. 5, pp. 1745–1762, 1989.Google Scholar
  89. [Lei]
    Leitmann G., On one approach to the control of uncertain systems. Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 373–380, 1993.Google Scholar
  90. [Lev]
    Levin B.Ja., Distribution of Zeros of Entire Functions. Translations of Mathematical Monographs, Vol. 5, American Mathematical Society. Providence, Rhode Island, 1964.Google Scholar
  91. [Ll]
    Lloyd N.G., Degree Theory. Cambridge University Press. Cambridge, London, New York, Melbourne, 1978.Google Scholar
  92. [LCZ]
    Levkovich A., Cohen N., Zeheb E., A root distribution criterion for an interval polynomial in a sector. Preprint, 1994.Google Scholar
  93. [LNL]
    Li Y., Nagpal K.M., Lee E.B., Stability analysis of polynomials with coefficients in disks. IEEE Trans. Autom. Contr, Vol. AC-37, No. 4, pp. 509–513, 1992.Google Scholar
  94. [M]
    Martin J.M., State-space measures for stability robustness. IEEE Transactions on Automatic Control, Vol. 32, No. 6, pp. 509–512, 1987.Google Scholar
  95. [MAD]
    Minnichelli R.J., Anagnost J.J., Desoer C.A., An elementary proof of Kharitonov's stability theorem with extensions. IEEE Trans. Autom. Contr., Vol. AC-34, No. 9, pp. 995–998, 1989.Google Scholar
  96. [MZJ]
    Malek-Zavarei M., Jamshidi M., Time-Delay Systems. Analysis, Optimization and Applications. North-Holland Systems and Control Series, Vol. 9. North-Holland, Amsterdam, New York, Oxford, Tokyo, 1987.Google Scholar
  97. [Nei]
    Neimark Y.I., Stability of Linearized Systems (in Russian). Leningrad, LKVVIA, 1949.Google Scholar
  98. [Nem]
    Nemirovskii A., Several NP-hard problems arising in robust stability analysis. Math. Contr., Signals Syst. Vol. 6, pp. 99–105, 1994.Google Scholar
  99. [NN]
    Nesterov Yu., Nemirovskii A., Interior-Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied Mathematics, Vol. 13, 1994.Google Scholar
  100. [P]
    Pontryagin L.S., On zeros of some elementary transcendental functions. Translations of AMS, Ser. 2, Vol. 1, pp. 95–110, 1955.Google Scholar
  101. [Pe]
    Petersen I.R., A class of stability regions for which a Kharitonov-like theorem hold. IEEE Trans. Autom. Contr., Vol. AC-34, No. 9, pp. 1111–1115, 1989.Google Scholar
  102. [Po]
    Polyak B.T., Robustness analysis for multilinear perturbations, pp. 93–104 in Robustness of Dynamic Systems with Parameter Uncertainties. Mansour M., Balemi S., Truol W., (editors). Monte Verità, Birkhäuser Verlag Basel, 1992.Google Scholar
  103. [PD]
    Packard A., Doyle J., Complex structural singular value. Automatica, Vol. 29, No. 9, pp. 71–110, 1993.Google Scholar
  104. [PK]
    Polyak B.T., Kogan J., Necessary and sufficient conditions for robust stability of multiaffine systems. Mathematics Research Report 93-06, Department of Mathematics, University of Maryland Baltimore County.Google Scholar
  105. [PL]
    Polyak B.T., Lan L.H., Value set of transfer functions with parametric uncertainty and their applications in robustness analysis. Preprint, 1993.Google Scholar
  106. [PS]
    Polya G., Szegö G., Problems and Theorems in Analysis, Vol. I. Springer, Berlin, 1972.Google Scholar
  107. [PT1]
    Polyak B.T., Tsypkin Ya.Z., Frequency criteria of robust stability and aperiodicity of linear systems. Automation and Remote Control, Vol. 51, No. 9, Part 1, pp. 1192–1201, 1990.Google Scholar
  108. [PT2]
    Polyak B.T., Tsypkin Ya.Z., Robust stability under complex perturbations of parameters. Automation and Remote Control, Vol. 52, No. 8, Part 1, pp. 1069–1077, 1991.Google Scholar
  109. [PT3]
    Polyak B.T., Tsypkin Ya.Z., Robust stability of the linear discrete systems. Dokl. Acad. Nauk, Vol. 316, No. 4, pp. 842–845, 1991, (in Russian).Google Scholar
  110. [PDB]
    Packard A., Doyle J., Balas G., Linear, multivariate robust control with a μ perspective. Transactions of the ASME, Journal of Dynamic Systems, Measurement, and Control, Vol. 115, pp. 426–438, 1993.Google Scholar
  111. [QD]
    Qiu L., Davison E.J., A unified approach for the stability robustness of polynomials in a convex set. Automatica, Vol. 28, No. 5, pp. 945–959, 1992.Google Scholar
  112. [QBRDYD]
    Qiu L., Bernhardsson B., Rantzer A., Davison E.J., Young P.M., Doyle J.C., A formula for computation of the real stability radius. Preprint, 1993.Google Scholar
  113. [Ra1]
    Rantzer A., Kharitonov's weak theorem holds if and only if the stability region and its reciprocal are convex. Int. J. of Nonlinear and Robust Contr., Vol. 3, pp. 55–62, 1993.Google Scholar
  114. [Ra2]
    Rantzer A., Stability conditions for polytopes of polynomials. IEEE Trans. Autom. Contr., Vol. AC-37, No. 1, pp. 79–89, 1992.Google Scholar
  115. [Ro]
    Rockafellar R.T., Convex Analysis. Princeton University Press, 1970.Google Scholar
  116. [Ru]
    Rudin W., Real and Complex Analysis. McGraw-Hill, New York, 1987.Google Scholar
  117. [RJ]
    Reddy H.C., Jury E.I., Study of the BIBO stability of 2-D recursive digital filters in the presence of nonessential signularities of the second kind-analog approach. IEEE Trans. Circuits Syst., Vol. CAS-34, No. 3, pp. 280–284, 1987.Google Scholar
  118. [RDC]
    Robledo C., Desages A., Cendra H., On the distance to the instability border of Hurwitz polynomials that depend affinely on m parameters and a particular convexity property of H n. Multidimensional Systems and Signal Processing, Vol. 3, No. 1, pp. 45–62, 1992.Google Scholar
  119. [Š]
    Šiljak D., Nonlinear Systems, the Parameter Analysis and Design. Wiley, New York, 1969.Google Scholar
  120. [Sa]
    Saeki M., A method of robust stability analysis with highly structured uncertainties. IEEE Trans. Autom. Contr., Vol. AC-31, No. 10, pp. 935–940, 1986.Google Scholar
  121. [Sc]
    Schwengeler E., Geometrisches über die Verteilung der Nullstellen spezieller ganzer Funktionen (Exponentialsummen). Dissertation, Zurich, 1925.Google Scholar
  122. [Sh]
    Shcherbakov P.S., Alexander Mikhailovitch Lyapunov: On the centenary of his doctoral dissertation on stability of motion. Automatica, Vol. 28, No. 5, pp. 865–871, 1992.Google Scholar
  123. [Si]
    Silkowski R., A star-shaped condition for stability of linear retarded functional differential equations. Proceedings of the Royal Society of Edinburgh, Vol. 83A, pp. 189–198, 1979.Google Scholar
  124. [Sk]
    Skorodinskii V.I., Iterational method of construction of Lyapunov-Krasovskii functionals for linear systems with delay. Automation and Remote Control, Vol. 51, No. 9, pp. 1205–1212, 1990.Google Scholar
  125. [St]
    Stépán G., Retarded Dynamical Systems: Stability and Characteristic Functions. π Pitman Research Notes in Mathematics Series: 210, 1989.Google Scholar
  126. [SZ]
    Shi Y.D., Zhou S.F., Stability of a set of multivariate complex polynomials with coefficients varying in a diamond domain. IEEE Trans. Circuits Syst., Vol. CAS-39, No. 8, pp. 683–688, 1992.Google Scholar
  127. [SEP1]
    Soh Y.C., Evans R.J., Petersen I.R., Characterization of a family of polynomials with interval roots. Technical Report EE8543, University of Newcastle, Newcastle, Australia, 1985.Google Scholar
  128. [SEP2]
    Soh Y.C., Evans R.J., Petersen I.R., A class of polynomials with multilinear parameter perturbations. Preprint, 1992.Google Scholar
  129. [SRP]
    Swamy M.N., Roytman L.M., Plotkin E.I., Planar least squares inverse polynomials and practical-BIBO stabilization of n-dimensional linear shift-invariant filters. IEEE Trans. Circuits Syst., Vol. CAS-32, No. 12, pp. 1255–1260, 1985.Google Scholar
  130. [SEPB]
    Soh Y.C., Evans R.J., Petersen I.R., Betz R.E., Robust pole assignment. Automatica, Vol. 23, No. 5, pp. 601–610, 1987.Google Scholar
  131. [Te]
    Tempo R., A dual result to Kharitonov's theorem. IEEE Trans. Autom. Contr., Vol. AC-35, No. 2, pp. 195–198, 1990.Google Scholar
  132. [Ti]
    Titchmarsh E.C., The Theory of Functions. Oxford University Press, London, 1962.Google Scholar
  133. [TF]
    Tsypkin Ya.Z., Fu M., Robust stability of time-delay systems with an uncertain time-delay constant. Int. J. Contr., Vol. 57, No. 4, pp. 865–879, 1993.Google Scholar
  134. [TK]
    Teboulle M., Kogan J., Applications of optimization methods to robust stability of linear systems. Journal of Optimization Theory and Applications, Vol. 81, No. 1, 1994, pp. 169–192.Google Scholar
  135. [TP1]
    Tsypkin Ya.Z., Polyak B.T., Frequency domain approach to robust stability of continuous systems, pp. 389–399 in Systems and Control: Topics in Theory and Applications. Kozin F., Ono T., (eds.), MITA Press, Osaka, 1991.Google Scholar
  136. [TP2]
    Tsypkin Ya.Z., Polyak B.T., Frequency domain criteria for l p-robust stability of continuous linear systems. IEEE Trans. Autom. Contr., Vol. AC-36, No. 12, pp. 1464–1469, 1991.Google Scholar
  137. [TT]
    Tsing N.-K., Tits A., When is a multiaffine image of a cube a polygon? Systems and Control Letters, Vol. 20, pp. 439–445, 1993.Google Scholar
  138. [TVZ]
    Tesi A., Vicino A., Zappa G., Clockwise property of the Nyquist plot with implications for absolute stability. Automatica, Vol. 28, No. 1, pp. 71–80, 1992.Google Scholar
  139. [WF]
    Wang S., Fairman F.W., On the simultaneous robust stabilization of three plants. Int. J. Contr., Vol. 59, No. 2, pp. 1095–1106, 1994.Google Scholar
  140. [WH]
    Wang L., Huang L., Robust stability of diamond families of polynomials with complex coefficients. Int. J. Systems Sci., Vol. 3, No. 8, pp. 1371–1378, 1992.Google Scholar
  141. [XF]
    Xin X., Feng C.-B., Robust stability of control systems with parametric uncertainties. Proceedings of the 31th IEEE Conference on Decision and Control, Tucson, Arizona, pp. 1559–1562, 1992.Google Scholar
  142. [Z]
    Zeheb E., Necessary and sufficient conditions for robust stability of a continuous systems-the continuous dependency case illustrated via multilinear dependency. IEEE Trans. on Circuits and Systems, Vol. 37, No. 1, pp. 47–53, 1990.Google Scholar
  143. [ZD]
    Zadeh L., Desoer C.A., Linear System Theory. McGraw Hill, NY, 1963.Google Scholar
  144. [ZW]
    Zeheb E., Walach E., Zero sets of multiparameter functions and stability of multidimensional systems. IEEE Trans. Acous., Speech, Sig. Processing, ASSP-29, pp. 197–206, 1981.Google Scholar

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