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Volumn 27, Issue 3, 2004, Pages 431-437

A unified approach to eigenvalue bounds of the solution of the Riccati equation

Author keywords

Eigenvalue bound; Unified Riccati equation

Indexed keywords

COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; PROBLEM SOLVING; RICCATI EQUATIONS; THEOREM PROVING;

EID: 2542447199     PISSN: 02533839     EISSN: 21587299     Source Type: Journal    
DOI: 10.1080/02533839.2004.9670889     Document Type: Article
Times cited : (8)

References (26)
  • 1
    • 84950962048 scopus 로고
    • Extreme Properties of Eigen-values of a Hermitian Transformation and Singular Values of the Sum and Product of Linear Transformations
    • Amir-Moez, R., 1956. “Extreme Properties of Eigen-values of a Hermitian Transformation and Singular Values of the Sum and Product of Linear Transformations,”. Duke Mathematical Journal, 23:463–467.
    • (1956) Duke Mathematical Journal , vol.23 , pp. 463-467
    • Amir-Moez, R.1
  • 2
    • 0035280033 scopus 로고    scopus 로고
    • Upper Matrix Bounds for the Discrete Algebraic Riccati Matrix Equation
    • Choi, H. H., 2001. “Upper Matrix Bounds for the Discrete Algebraic Riccati Matrix Equation,”. IEEE Transactions on Automatic Control, 46 (3):504–508.
    • (2001) IEEE Transactions on Automatic Control , vol.46 , Issue.3 , pp. 504-508
    • Choi, H.H.1
  • 3
    • 0036642648 scopus 로고    scopus 로고
    • Lower Matrix Bounds for the Continuous Algebraic Riccati and Lyapunov Matrix Equations
    • Choi, H. H., and Kuc, T. Y., 2002. “Lower Matrix Bounds for the Continuous Algebraic Riccati and Lyapunov Matrix Equations,”. Automatica, 38 (7):1147–1152.
    • (2002) Automatica , vol.38 , Issue.7 , pp. 1147-1152
    • Choi, H.H.1    Kuc, T.Y.2
  • 4
    • 0022663313 scopus 로고
    • Bounds for the Eigenvalues of the Solution of Discrete Riccati and Lyapunov Equations and the Continuous Lyapunov Equation
    • Garloff, J., 1986. “Bounds for the Eigenvalues of the Solution of Discrete Riccati and Lyapunov Equations and the Continuous Lyapunov Equation,”. International Journal of Control, 43 (2):423–431.
    • (1986) International Journal of Control , vol.43 , Issue.2 , pp. 423-431
    • Garloff, J.1
  • 5
    • 0020633404 scopus 로고
    • A Note on Eigenvalue Bounds in Algebraic Riccati Equation
    • Karanam, V. R., 1983. “A Note on Eigenvalue Bounds in Algebraic Riccati Equation,”. IEEE Transactions on Automatic Control, 28 (1):109–111.
    • (1983) IEEE Transactions on Automatic Control , vol.28 , Issue.1 , pp. 109-111
    • Karanam, V.R.1
  • 6
    • 0012589524 scopus 로고    scopus 로고
    • Matrix Bounds of the Discrete ARE Solution
    • Kim, S. W., and Park, P. G., 1999. “Matrix Bounds of the Discrete ARE Solution,”. Systems and Control Letters, 36 (1):15–20.
    • (1999) Systems and Control Letters , vol.36 , Issue.1 , pp. 15-20
    • Kim, S.W.1    Park, P.G.2
  • 7
    • 0028493597 scopus 로고
    • Iterative Matrix Bounds and Computational Solutions to the Discrete Algebraic Riccati Equation
    • Komaroff, N., 1994. “Iterative Matrix Bounds and Computational Solutions to the Discrete Algebraic Riccati Equation,”. IEEE Transactions on Automatic Control, 39 (8):1676–1678.
    • (1994) IEEE Transactions on Automatic Control , vol.39 , Issue.8 , pp. 1676-1678
    • Komaroff, N.1
  • 8
    • 0026885001 scopus 로고
    • Lower Summation Bounds for the Discrete Riccati and Lyapunov Equations
    • Komaroff, N., and Shahian, B., 1992. “Lower Summation Bounds for the Discrete Riccati and Lyapunov Equations,”. IEEE Transactions on Automatic Control, 37 (7):1078–1080.
    • (1992) IEEE Transactions on Automatic Control , vol.37 , Issue.7 , 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
    • Kouikoglou, V. S., and Phillis, Y. A., 1993. “Trace Bounds on the Covariances of Continuous-Time Systems with Multiplicative Noise,”. IEEE Transactions on Automatic Control, 38 (1):138–142.
    • (1993) IEEE Transactions on Automatic Control , vol.38 , Issue.1 , pp. 138-142
    • Kouikoglou, V.S.1    Phillis, Y.A.2
  • 10
  • 11
    • 0030173646 scopus 로고    scopus 로고
    • Bounds in Algebraic Riccati and Lyapunov Equations: A Survey and Some New Results
    • Kwon, W. H., Moon, Y. S., and Ahn, S. C., 1996. “Bounds in Algebraic Riccati and Lyapunov Equations:A Survey and Some New Results,”. International Journal of Control, 64 (3):377–389.
    • (1996) International Journal of Control , vol.64 , Issue.3 , pp. 377-389
    • Kwon, W.H.1    Moon, Y.S.2    Ahn, S.C.3
  • 12
    • 0000419405 scopus 로고
    • A Note on the Algebraic Matrix Riccati Equation
    • Kwon, W. H., and Pearson, A. E., 1977. “A Note on the Algebraic Matrix Riccati Equation,”. IEEE Transactions on Automatic Control, 22 (2):143–144.
    • (1977) IEEE Transactions on Automatic Control , vol.22 , Issue.2 , pp. 143-144
    • Kwon, W.H.1    Pearson, A.E.2
  • 13
    • 0030144629 scopus 로고    scopus 로고
    • On the Matrix Bounds for the Solution of the Discrete Algebraic Riccati Equation
    • part-I
    • Lee, C. H., 1996. “On the Matrix Bounds for the Solution of the Discrete Algebraic Riccati Equation,”. IEEE Transactions on Circuits and Systems, 43 (5):402–407. part-I
    • (1996) IEEE Transactions on Circuits and Systems , vol.43 , Issue.5 , pp. 402-407
    • Lee, C.H.1
  • 14
    • 0030781908 scopus 로고    scopus 로고
    • "On the Upper and Lower Bounds of the Solution for the Continuous Riccati Matrix Equation
    • Lee, C. H., 1997a. "On the Upper and Lower Bounds of the Solution for the Continuous Riccati Matrix Equation,”. International Journal of Control, 66 (1):105–118.
    • (1997) International Journal of Control , vol.66 , Issue.1 , pp. 105-118
    • Lee, C.H.1
  • 15
    • 0031251311 scopus 로고    scopus 로고
    • "Upper and Lower Bounds of the Solution of the Discrete Algebraic Riccati and Lyapunov Matrix Equations
    • Lee, C. H., 1997b. "Upper and Lower Bounds of the Solution of the Discrete Algebraic Riccati and Lyapunov Matrix Equations,”. International Journal of Control, 68 (3):579–598.
    • (1997) International Journal of Control , vol.68 , Issue.3 , pp. 579-598
    • 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
    • Lee, C. H., 1997c. “New Results for the Bounds of the Solution for the Continuous Riccati and Lyapunov Equations,”. IEEE Transactions on Automatic Control, 42 (1):118–123.
    • (1997) IEEE Transactions on Automatic Control , vol.42 , Issue.1 , pp. 118-123
    • Lee, C.H.1
  • 17
    • 0032206178 scopus 로고    scopus 로고
    • Simple Stabilizability Criteria and Memoryless State Feedback Control Design for Time-Delay Systems with Time-Varying Perturbations
    • part-I
    • Lee, C. H., 1998. “Simple Stabilizability Criteria and Memoryless State Feedback Control Design for Time-Delay Systems with Time-Varying Perturbations,”. IEEE Transactions on Circuits and Systems, 45 (11):1121–1125. part-I
    • (1998) IEEE Transactions on Circuits and Systems , vol.45 , Issue.11 , pp. 1121-1125
    • Lee, C.H.1
  • 19
    • 84947372046 scopus 로고
    • A Brief Summary of the Bounds on the Solution of the Algebraic Equations in Control Theory
    • Mori, T., and Derese, I. A., 1984. “A Brief Summary of the Bounds on the Solution of the Algebraic Equations in Control Theory,”. International Journal of Control, 39 (2):247–256.
    • (1984) International Journal of Control , vol.39 , Issue.2 , pp. 247-256
    • Mori, T.1    Derese, I.A.2
  • 20
    • 0029287966 scopus 로고
    • Bounds for the Eigenvalues of the Solution of the Unified Algebraic Riccati Matrix Equation
    • Mrabti, M., and Benseddik, M., 1995. “Bounds for the Eigenvalues of the Solution of the Unified Algebraic Riccati Matrix Equation,”. Systems and Control Letters, 24 (5):345–349.
    • (1995) Systems and Control Letters , vol.24 , Issue.5 , pp. 345-349
    • Mrabti, M.1    Benseddik, M.2
  • 21
    • 0026715709 scopus 로고
    • Bounds for the Solution of the Lyapunov Matrix Equation-A Unified Approach
    • Mrabti, M., and Hmamed, A., 1992. “Bounds for the Solution of the Lyapunov Matrix Equation-A Unified Approach,”. Systems and Control Letters, 18 (1):73–81.
    • (1992) Systems and Control Letters , vol.18 , Issue.1 , pp. 73-81
    • Mrabti, M.1    Hmamed, A.2
  • 22
    • 0022757579 scopus 로고
    • Trace Bounds on the Solution of the Algebraic Matrix Riccati and Lyapunov Equations
    • Wang, S. D., Kuo, T. S., and Hsu, C. F., 1986. “Trace Bounds on the Solution of the Algebraic Matrix Riccati and Lyapunov Equations,”. IEEE Transactions on Automatic Control, 31 (7):654–656.
    • (1986) IEEE Transactions on Automatic Control , vol.31 , Issue.7 , pp. 654-656
    • Wang, S.D.1    Kuo, T.S.2    Hsu, C.F.3
  • 23
    • 0023412541 scopus 로고
    • Robust Stability of Uncertain Time-Delay Systems
    • Wang, S. S., Chen, B. S., and Lin, T. P., 1987. “Robust Stability of Uncertain Time-Delay Systems,”. International Journal of Control, 46 (3):963–976.
    • (1987) International Journal of Control , vol.46 , Issue.3 , pp. 963-976
    • Wang, S.S.1    Chen, B.S.2    Lin, T.P.3
  • 24
    • 0018478436 scopus 로고
    • Upper and Lower Bounds on the Solution of the Algebraic Riccati Equation
    • Yasuda, K., and Hirai, K., 1979. “Upper and Lower Bounds on the Solution of the Algebraic Riccati Equation,”. IEEE Transactions on Automatic Control, 24 (3):483–487.
    • (1979) IEEE Transactions on Automatic Control , vol.24 , Issue.3 , pp. 483-487
    • Yasuda, K.1    Hirai, K.2
  • 25
    • 0020707190 scopus 로고
    • A Priori Bound for Optimal Stochastic Control Problem with Multiplicative Noise
    • Yaz, E., 1983. “A Priori Bound for Optimal Stochastic Control Problem with Multiplicative Noise,”. Electronics Letters, 19 (4):1137–1139.
    • (1983) Electronics Letters , vol.19 , Issue.4 , pp. 1137-1139
    • Yaz, E.1
  • 26
    • 0022098534 scopus 로고
    • Bounds for the Eigenvalues of the Solution Matrix of the Algebraic Riccati Equation
    • Yaz, E., 1985. “Bounds for the Eigenvalues of the Solution Matrix of the Algebraic Riccati Equation,”. International Journal of Systems and Science, 16 (7):815–820.
    • (1985) International Journal of Systems and Science , vol.16 , Issue.7 , pp. 815-820
    • Yaz, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.