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Volumn 48, Issue 8, 2003, Pages 1409-1413

Solution bounds of the continuous Riccati matrix equation

(1)  Lee, Chien Hua a  

a NONE

Author keywords

Continuous algebraic Riccati equation; Eigenvalue bounds; Matrix bounds

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 0042382883     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.815029     Document Type: Article
Times cited : (21)

References (25)
  • 1
    • 0036642648 scopus 로고    scopus 로고
    • Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations
    • H. H. Choi and T. Y. Kue, "Lower matrix bounds for the continuous algebraic Riccati and Lyapunov matrix equations," Automatica, vol. 38, pp. 1147-1152, 2002.
    • (2002) Automatica , vol.38 , pp. 1147-1152
    • Choi, H.H.1    Kue, T.Y.2
  • 2
    • 0022663313 scopus 로고
    • Bounds for the eigenvalues of the solution of discrete Riccati and Lyapunov equations and the continuous Lyapunov equation
    • J. Garloff, "Bounds for the eigenvalues of the solution of discrete Riccati and Lyapunov equations and the continuous Lyapunov equation," Int. J. Control, vol. 43, pp. 423-431, 1986.
    • (1986) Int. J. Control , vol.43 , pp. 423-431
    • Garloff, J.1
  • 3
    • 0006110024 scopus 로고
    • On bounds of Lyapunov's matrix equation
    • June
    • J. C. Geromel and J. Bernussou, "On bounds of Lyapunov's matrix equation," IEEE Trans. Automat. Contr., vol. AC-24, pp. 482-483, June 1979.
    • (1979) IEEE Trans. Automat. Contr. , vol.AC-24 , pp. 482-483
    • Geromel, J.C.1    Bernussou, J.2
  • 4
    • 0026170257 scopus 로고
    • Discrete Lyapunov equation: Simultaneous eigenvalue lower bounds
    • A. Hmamed, "Discrete Lyapunov equation: Simultaneous eigenvalue lower bounds," Int. J. Syst. Sci., vol. 22, pp. 1121-1126, 1991.
    • (1991) Int. J. Syst. Sci. , vol.22 , pp. 1121-1126
    • Hmamed, A.1
  • 5
    • 0012589524 scopus 로고    scopus 로고
    • Matrix bounds of the discrete ARE solution
    • S. W. Kim and P. G. Park, "Matrix bounds of the discrete ARE solution," Syst. Control Lett., vol. 36, pp. 15-20, 1999.
    • (1999) Syst. Control Lett. , vol.36 , pp. 15-20
    • Kim, S.W.1    Park, P.G.2
  • 6
    • 0026927361 scopus 로고
    • Upper bounds for the solution of the discrete Riccati equation
    • Sept.
    • N. Komaroff, "Upper bounds for the solution of the discrete Riccati equation," IEEE Trans. Automat. Contr., vol. 37, pp. 1370-1373, Sept. 1992.
    • (1992) IEEE Trans. Automat. Contr. , vol.37 , pp. 1370-1373
    • Komaroff, N.1
  • 7
    • 0028493597 scopus 로고
    • Iterative matrix bounds and computational solutions to the discrete algebraic Riccati equation
    • Aug.
    • ____, "Iterative matrix bounds and computational solutions to the discrete algebraic Riccati equation," IEEE Trans. Automat. Contr., vol. 39, pp. 1676-1678, Aug. 1994.
    • (1994) IEEE Trans. Automat. Contr. , vol.39 , pp. 1676-1678
    • Komaroff, N.1
  • 8
    • 0026885001 scopus 로고
    • Lower summation bounds for the discrete Riccati and Lyapunov equations
    • July
    • N. Komaroff and B. Shahian, "Lower summation bounds for the discrete Riccati and Lyapunov equations," IEEE Trans. Automat. Contr., vol. 37, pp. 1078-1080, July 1992.
    • (1992) IEEE Trans. Automat. Contr. , vol.37 , pp. 1078-1080
    • Komaroff, N.1    Shahian, B.2
  • 9
    • 0027239302 scopus 로고
    • Trace bounds on the covariances of continuous-time systems with multiplicative noise
    • Jan.
    • V. S. Kouikoglou and Y. A. Phillis, "Trace bounds on the covariances of continuous-time systems with multiplicative noise," IEEE Trans. Automat. Contr., vol. 38, pp. 138-142, Jan. 1993.
    • (1993) IEEE Trans. Automat. Contr. , vol.38 , pp. 138-142
    • Kouikoglou, V.S.1    Phillis, Y.A.2
  • 10
    • 0015300451 scopus 로고
    • Conditions for nonnegativeness of portioned matrices
    • Feb.
    • E. Kreindler and A. Jameson, "Conditions for nonnegativeness of portioned matrices," IEEE Trans. Automat. Contr., vol. AC-17, pp. 147-148, Feb. 1972.
    • (1972) IEEE Trans. Automat. Contr. , vol.AC-17 , pp. 147-148
    • Kreindler, E.1    Jameson, A.2
  • 11
    • 0030173646 scopus 로고    scopus 로고
    • Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results
    • W. H. Kwon, Y. S. Moon, and S. C. Ahn, "Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results," Int. J. Control, vol. 64, pp. 377-389, 1996.
    • (1996) Int. J. Control , vol.64 , pp. 377-389
    • Kwon, W.H.1    Moon, Y.S.2    Ahn, S.C.3
  • 12
    • 0022147869 scopus 로고
    • On bounds of the Riccati and Lyapunov equations
    • Nov.
    • B. H. Kwon, M. J. Youn, and Z. Bien, "On bounds of the Riccati and Lyapunov equations," IEEE Trans. Automat. Contr., vol. AC-30, pp. 1134-1135, Nov. 1985.
    • (1985) IEEE Trans. Automat. Contr. , vol.AC-30 , pp. 1134-1135
    • Kwon, B.H.1    Youn, M.J.2    Bien, Z.3
  • 13
    • 0031251311 scopus 로고    scopus 로고
    • Upper and lower bounds of the solutions of the discrete algebraic Riccati and Lyapunov matrix equations
    • C. H. Lee, "Upper and lower bounds of the solutions of the discrete algebraic Riccati and Lyapunov matrix equations," Int. J. Control, vol. 68, pp. 579-598, 1997.
    • (1997) Int. J. Control , vol.68 , pp. 579-598
    • Lee, C.H.1
  • 14
    • 0041588943 scopus 로고    scopus 로고
    • Eigenvalue upper and lower bounds of the solution for the continuous algebraic matrix Riccati equation
    • Aug.
    • ____, "Eigenvalue upper and lower bounds of the solution for the continuous algebraic matrix Riccati equation," IEEE Trans. Circuits Syst. I, vol. 43, pp. 683-686, Aug. 1996.
    • (1996) IEEE Trans. Circuits Syst. I , vol.43 , pp. 683-686
    • Lee, C.H.1
  • 15
    • 0030244351 scopus 로고    scopus 로고
    • Upper and lower matrix bounds of the solution for the discrete Lyapunov equation
    • Sept.
    • ____, "Upper and lower matrix bounds of the solution for the discrete Lyapunov equation," IEEE Trans. Automat. Contr., vol. 41, pp. 1338-1341, Sept. 1996.
    • (1996) IEEE Trans. Automat. Contr. , vol.41 , pp. 1338-1341
    • Lee, C.H.1
  • 16
    • 0030846963 scopus 로고    scopus 로고
    • New results for the bounds of the solution for the continuous Riccati and Lyapunov equations
    • Jan.
    • ____, "New results for the bounds of the solution for the continuous Riccati and Lyapunov equations," IEEE Trans. Automat. Contr., vol. 42, pp. 118-123, Jan. 1997.
    • (1997) IEEE Trans. Automat. Contr. , vol.42 , pp. 118-123
    • Lee, C.H.1
  • 17
    • 0030781908 scopus 로고    scopus 로고
    • On the upper and lower bounds of the solution for the continuous Riccati matrix equation
    • ____, "On the upper and lower bounds of the solution for the continuous Riccati matrix equation," Int. J. Control, vol. 66, pp. 105-118, 1997.
    • (1997) Int. J. Control , vol.66 , pp. 105-118
    • Lee, C.H.1
  • 18
    • 0035838739 scopus 로고    scopus 로고
    • On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems
    • C. H. Lee and S. T. Lee, "On the estimation of solution bounds of the generalized Lyapunov equations and the robust root clustering for the linear perturbed systems," Int. J. Control, vol. 74, pp. 996-1008, 2001.
    • (2001) Int. J. Control , vol.74 , pp. 996-1008
    • Lee, C.H.1    Lee, S.T.2
  • 19
    • 0027668155 scopus 로고
    • A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays
    • Sept.
    • C. H. Lee, T.-H. S. Li, and F. C. Kung, "A new approach for the robust stability of perturbed systems with a class of noncommensurate time delays," IEEE Trans. Circuits Syst. I, vol. 40, pp. 605-608, Sept. 1993.
    • (1993) IEEE Trans. Circuits Syst. I , vol.40 , pp. 605-608
    • Lee, C.H.1    Li, T.-H.S.2    Kung, F.C.3
  • 21
    • 0021373893 scopus 로고
    • A brief summary of the bounds on the solution of the algebraic equations in control theory
    • T. Mori and I. A. Derese, "A brief summary of the bounds on the solution of the algebraic equations in control theory," Int. J. Control, vol. 39, pp. 247-256, 1984.
    • (1984) Int. J. Control , vol.39 , pp. 247-256
    • Mori, T.1    Derese, I.A.2
  • 22
    • 0023399802 scopus 로고
    • Improved bounds for the eigenvalues of solutions of Lyapunov equation
    • Aug.
    • I. Troch, "Improved bounds for the eigenvalues of solutions of Lyapunov equation," IEEE Trans. Automat. Contr., vol. AC-32, pp. 744-747, Aug. 1987.
    • (1987) IEEE Trans. Automat. Contr. , vol.AC-32 , pp. 744-747
    • Troch, I.1
  • 23
    • 0023412541 scopus 로고
    • Robust stability of uncertain time-delay systems
    • S. S. Wang and T. P. Lin, "Robust stability of uncertain time-delay systems," Int. J. Control, vol. 46, pp. 963-976, 1987.
    • (1987) Int. J. Control , vol.46 , pp. 963-976
    • Wang, S.S.1    Lin, T.P.2
  • 24
    • 0022757579 scopus 로고
    • Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equations
    • July
    • S. D. Wang, T. S. Kuo, and C. F. Hsu, "Trace bounds on the solution of the algebraic matrix Riccati and Lyapunov equations," IEEE Trans. Automat. Contr., vol. AC-31, pp. 654-656, July 1986.
    • (1986) IEEE Trans. Automat. Contr. , vol.AC-31 , pp. 654-656
    • Wang, S.D.1    Kuo, T.S.2    Hsu, C.F.3
  • 25
    • 0027190083 scopus 로고
    • Robust root clustering for linear uncertain systems using generalized Lyapunov theory
    • R. K. Yedavalli, "Robust root clustering for linear uncertain systems using generalized Lyapunov theory," Automatica, vol. 29, pp. 237-240, 1993.
    • (1993) Automatica , vol.29 , pp. 237-240
    • Yedavalli, R.K.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.