메뉴 건너뛰기




Volumn 26, Issue 4, 1981, Pages 853-863

A General Theory for Matrix Root-Clustering in Subregions of the Complex Plane

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL SYSTEMS;

EID: 0019601242     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/TAC.1981.1102764     Document Type: Article
Times cited : (225)

References (42)
  • 1
    • 0006753330 scopus 로고
    • Leyden France: Maire, (Translation: The Geometry of René Descartes. La Salle, France: Open Court, 1925.)
    • R. Descartes, La Géométrie. Leyden France: Maire, 1637. (Translation: The Geometry of René Descartes. La Salle, France: Open Court, 1925.)
    • (1637) La Géométrie
    • Descartes, R.1
  • 3
    • 79953298368 scopus 로고
    • Analyse d'un mémoire sur la résolution des équations numériques
    • C. Sturm “Analyse d'un mémoire sur la résolution des équations numériques,” Bull. Sci. Math. Ferussac. vol. II, pp. 419–422, 1829.
    • (1829) Bull. Sci. Math. Ferussac. , vol.2 , pp. 419-422
    • Sturm, C.1
  • 4
    • 0011452575 scopus 로고
    • On the number of roots of an algebraic equation contained between given limits
    • also in Int. J. Contr., vol. 26, pp. 183–195. 1977 (P.C. Parks, Trans.)
    • C. Hermite. “On the number of roots of an algebraic equation contained between given limits.” J. Reine Augew. Math., vol. 52, pp. 39–51. 1856; also in Int. J. Contr., vol. 26, pp. 183–195. 1977 (P.C. Parks, Trans.).
    • (1856) J. Reine Augew. Math. , vol.52 , pp. 39-51
    • Hermite, C.1
  • 6
    • 0001440029 scopus 로고
    • Über die bedingungen, unter welchem eine gleichung nur wurzeln mit negativen relen teilen besitzt
    • A. Hurwitz “Über die bedingungen, unter welchem eine gleichung nur wurzeln mit negativen relen teilen besitzt,” Math. Ann., vol. 46, pp. 273–284, 1895.
    • (1895) Math. Ann. , vol.46 , pp. 273-284
    • Hurwitz, A.1
  • 7
    • 0009351736 scopus 로고
    • Sur le signe de la partie réelle des racines d'une équation algébrique
    • A. Liénard and M. H. Chipart “Sur le signe de la partie réelle des racines d'une équation algébrique.” J. Math. Pure Appt., vol. 10, pp. 291–346, 1914.
    • (1914) J. Math. Pure Appt. , vol.10 , pp. 291-346
    • Liénard, A.1    Chipart, M.H.2
  • 8
    • 0001065170 scopus 로고
    • Über die anzahl der wurzeln einer algebraischen gleichung in einer kreise
    • A. Cohn, “Über die anzahl der wurzeln einer algebraischen gleichung in einer kreise.” Math. Z., vol. 14–15, pp. 110–148. 1914.
    • (1914) Math. Z. , vol.14-14 , pp. 110-148
    • Cohn, A.1
  • 9
    • 0015080919 scopus 로고
    • Inners, approach to some problems of system theory
    • June
    • E. I. Jury. “Inners, approach to some problems of system theory.” IEEE Trans. Automat. Contr., vol. AC-16, pp. 233–240, June 1971.
    • (1971) IEEE Trans. Automat. Contr. , vol.AC-16 , pp. 233-240
    • Jury, E.I.1
  • 14
    • 0000297337 scopus 로고
    • Algebraic characterization of polynomials whose zeros lie in a certain algebraic domain
    • May
    • R. E. Kalman, “Algebraic characterization of polynomials whose zeros lie in a certain algebraic domain,” Proc. Nat. Acad. Sci., vol. 64, pp. 818–823, May 1969.
    • (1969) Proc. Nat. Acad. Sci. , vol.64 , pp. 818-823
    • Kalman, R.E.1
  • 15
    • 0015354091 scopus 로고
    • Symmetric and innerwise matrices for the root clustering and root distribution of a polynomial
    • June
    • E. I. Jury and S. M. Ahn. “Symmetric and innerwise matrices for the root clustering and root distribution of a polynomial,” J. Franklin Inst., vol. 293, pp. 433–450, June 1972.
    • (1972) J. Franklin Inst. , vol.293 , pp. 433-450
    • Jury, E.I.1    Ahn, S.M.2
  • 16
    • 0016473153 scopus 로고
    • A note on matrix equations and root location
    • Feb.
    • S. Barnett “A note on matrix equations and root location,” IEEE Trans. Automat. Contr., vol. AC-20, pp. 158–159, Feb. 1975.
    • (1975) IEEE Trans. Automat. Contr. , vol.AC-20 , pp. 158-159
    • Barnett, S.1
  • 17
    • 0018468563 scopus 로고
    • Root clustering of a real matrix in an algebraic region
    • S. Gutman. “Root clustering of a real matrix in an algebraic region.” Int. J. Contr., vol. 29, pp. 871–880. 1979.
    • (1979) Int. J. Contr. , vol.29 , pp. 871-880
    • Gutman, S.1
  • 18
    • 0018503485 scopus 로고
    • Root clustering of a complex matrix in an algebraic region
    • Aug.
    • S. Gutman “Root clustering of a complex matrix in an algebraic region,” IEEE Trans. Automat. Contr., vol. AC-24, pp. 647–650, Aug. 1979.
    • (1979) IEEE Trans. Automat. Contr. , vol.AC-24 , pp. 647-650
    • Gutman, S.1
  • 19
    • 0010715828 scopus 로고
    • Remarks on the root clustering of a polynomial in a certain region in the complex plane
    • July
    • E. I. Jury and S. M. Ahn, “Remarks on the root clustering of a polynomial in a certain region in the complex plane,” Quart. Appl. Math., pp. 203–205, July 1974.
    • (1974) Quart. Appl. Math. , pp. 203-205
    • Jury, E.I.1    Ahn, S.M.2
  • 22
    • 0017502391 scopus 로고
    • Output feedback stabilization-solution by algebraic geometry methods
    • June
    • B. D. O. Anderson and R. W. Scott, “Output feedback stabilization-solution by algebraic geometry methods,” Proc. IEEE. vol. 65, pp. 849–861, June 1977.
    • (1977) Proc. IEEE. , vol.65 , pp. 849-861
    • Anderson, B.D.O.1    Scott, R.W.2
  • 23
    • 84944481457 scopus 로고
    • On the minimal information necessary to stabilize a linear system
    • IIASA Rep. RR-74-15, Austria, Sept.
    • J. Casti. “On the minimal information necessary to stabilize a linear system,” IIASA Rep. RR-74-15, Austria, Sept. 1974.
    • (1974)
    • Casti, J.1
  • 24
    • 84938006533 scopus 로고
    • Observers for multivariable systems
    • Apr.
    • D. G. Luenberger, “Observers for multivariable systems,” IEEE Trans. Automat. Contr., vol. AC-11, pp. 190–197. Apr. 1966.
    • (1966) IEEE Trans. Automat. Contr. , vol.AC-11 , pp. 190-197
    • Luenberger, D.G.1
  • 25
    • 0014732507 scopus 로고
    • Pole placement using dynamic compensators
    • Feb.
    • F. M. Brasch Jr., and J. B. Pearson “Pole placement using dynamic compensators,” IEEE Trans. Automat. Contr., vol. AC-15, pp. 34–43, Feb. 1970.
    • (1970) IEEE Trans. Automat. Contr. , vol.AC-15 , pp. 34-43
    • Brasch, F.M.1    Pearson, J.B.2
  • 27
    • 84944481458 scopus 로고
    • A criterion for choosing minimal feedback gains of relatively stable linear dynamical systems
    • M.Sc. thesis. Dep. Mechanical Eng., Technion, Israel Inst, of Technology. Nov.
    • G. Shwartz, “A criterion for choosing minimal feedback gains of relatively stable linear dynamical systems,” M.Sc. thesis. Dep. Mechanical Eng., Technion, Israel Inst, of Technology. Nov. 1979.
    • (1979)
    • Shwartz, G.1
  • 31
    • 0008525582 scopus 로고
    • Sur une extension du calcul des substitutions linéaires
    • C. Stéphanos, “Sur une extension du calcul des substitutions linéaires,” J. Math. Pures Appl. vol. 6, pp. 73–128, 1900.
    • (1900) J. Math. Pures Appl. , vol.6 , pp. 73-128
    • Stéphanos, C.1
  • 32
    • 0000321992 scopus 로고
    • Explicit solutions of linear matrix equations
    • Oct.
    • P. Lancaster, “Explicit solutions of linear matrix equations.” SIAM Rev., vol. 12, pp. 544–566. Oct. 1970.
    • (1970) SIAM Rev. , vol.12 , pp. 544-566
    • Lancaster, P.1
  • 34
    • 0010709426 scopus 로고
    • Matrix equations and the separation of matrix eigenvalues
    • J. L. Howland “Matrix equations and the separation of matrix eigenvalues,” J. Math. Anal. Appl., vol. 33, pp. 683–691, 1971.
    • (1971) J. Math. Anal. Appl. , vol.33 , pp. 683-691
    • Howland, J.L.1
  • 35
    • 0347049761 scopus 로고
    • Eigenvalue location using certain matrix functions and geometric curves
    • R. D. Hill, “Eigenvalue location using certain matrix functions and geometric curves,” Linear Algebra Appl., vol. 16, pp. 83–91. 1977.
    • (1977) Linear Algebra Appl. , vol.16 , pp. 83-91
    • Hill, R.D.1
  • 36
    • 0017951660 scopus 로고
    • On redundance in aperiodicity criteria
    • A. T. Fuller “On redundance in aperiodicity criteria,” J. Math. Anal. Appl., vol. 68, pp. 371–394, 1979.
    • (1979) J. Math. Anal. Appl. , vol.68 , pp. 371-394
    • Fuller, A.T.1
  • 37
    • 0018478342 scopus 로고
    • Remarks on redundance in stability criteria and a counterexample to Fuller's conjecture
    • A. Arapostathis, and E. I. Jury “Remarks on redundance in stability criteria and a counterexample to Fuller's conjecture,” Int. J. Contr., vol. 29, pp. 1027–1034, 1979.
    • (1979) Int. J. Contr. , vol.29 , pp. 1027-1034
    • Arapostathis, A.1    Jury, E.I.2
  • 38
    • 84944481460 scopus 로고
    • private communication, May
    • A. T. Fuller, private communication, May 1980.
    • (1980)
    • Fuller, A.T.1
  • 39
    • 33749921342 scopus 로고
    • Simplification of certain linear matrix equations
    • Feb.
    • S. Barnett “Simplification of certain linear matrix equations.” IEEE Trans. Automat. Contr., vol. AC-21, pp. 115–116, Feb. 1976.
    • (1976) IEEE Trans. Automat. Contr. , vol.AC-21 , pp. 115-116
    • Barnett, S.1
  • 40
    • 0016472847 scopus 로고
    • Output feedback stabilization and related problems—solution via decision methods
    • Feb.
    • B. D. O. Anderson, N. K. Bose, and E. I. Jury “Output feedback stabilization and related problems—solution via decision methods.” IEEE Trans. Automat. Contr., vol. AC-20, pp. 53–66, Feb. 1975.
    • (1975) IEEE Trans. Automat. Contr. , vol.AC-20 , pp. 53-66
    • Anderson, B.D.O.1    Bose, N.K.2    Jury, E.I.3
  • 41
    • 0017543034 scopus 로고
    • Regions of polynomical root clustering
    • Oct./Nov.
    • T. A. Bickart, and E. I. Jury, “Regions of polynomical root clustering,” J. Franklin Inst., vol. 304, pp. 149–160, Oct./Nov. 1977.
    • (1977) J. Franklin Inst. , vol.304 , pp. 149-160
    • Bickart, T.A.1    Jury, E.I.2
  • 42
    • 0018734576 scopus 로고
    • Eigenvalues of a matrix inside an ellipse and Chebvshev filter
    • Dec.
    • S. M. Ahn “Eigenvalues of a matrix inside an ellipse and Chebvshev filter,” IEEE Trans. Automat. Contr., vol. AC-24, pp. 986–987, Dec. 1979.
    • (1979) IEEE Trans. Automat. Contr. , vol.AC-24 , pp. 986-987
    • Ahn, S.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.