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Volumn 54, Issue 2, 2005, Pages 95-107

Iterative least-squares solutions of coupled Sylvester matrix equations

Author keywords

Estimation; Gauss Seidel iteration; Hadamard product; Hierarchical identification principle; Identification; Jacobi iteration; Least squares; Lyapunov matrix equation; Star product; Sylvester matrix equation

Indexed keywords

ALGORITHMS; ESTIMATION; HIERARCHICAL SYSTEMS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; PARAMETER ESTIMATION;

EID: 10444247504     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2004.06.008     Document Type: Article
Times cited : (400)

References (38)
  • 2
    • 0019689365 scopus 로고
    • Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations
    • R. Bitmead, Explicit solutions of the discrete-time Lyapunov matrix equation and Kalman-Yakubovich equations, IEEE Trans. Automat. Control 26 (1981) 1291-1294.
    • (1981) IEEE Trans. Automat. Control , vol.26 , pp. 1291-1294
    • Bitmead, R.1
  • 3
    • 0018480844 scopus 로고
    • On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form
    • R. Bitmead, H. Weiss, On the solution of the discrete-time Lyapunov matrix equation in controllable canonical form, IEEE Trans. Automat. Control 24 (1979) 481-482.
    • (1979) IEEE Trans. Automat. Control , vol.24 , pp. 481-482
    • Bitmead, R.1    Weiss, H.2
  • 4
    • 0029375701 scopus 로고
    • Parallel computation of the solutions of coupled algebraic Lyapunov equations
    • I. Borno, Parallel computation of the solutions of coupled algebraic Lyapunov equations, Automatica 31 (1995) 1345-1347.
    • (1995) Automatica , vol.31 , pp. 1345-1347
    • Borno, I.1
  • 6
    • 0028462341 scopus 로고
    • ∞ of general multirate sampled-data control systems
    • ∞ design of general multirate sampled-data control systems, Automatica 30 (l994) 139-1152.
    • (1994) Automatica , vol.30 , pp. 139-1152
    • Chen, T.1    Qiu, L.2
  • 7
    • 38149012697 scopus 로고
    • The solution of the matrix A X B - C X D = E and (YA - DZ, YC- BZ) = (E, F)
    • K.E. Chu, The solution of the matrix A X B - C X D = E and (YA - DZ, YC - BZ) = (E, F), Linear Algebra Appl. 93 (1987) 93-105.
    • (1987) Linear Algebra Appl. , vol.93 , pp. 93-105
    • Chu, K.E.1
  • 8
    • 0037906213 scopus 로고    scopus 로고
    • Convergence and comparison theorems for a generalized alternating iterative method
    • J.J. Climent, C. Perea, Convergence and comparison theorems for a generalized alternating iterative method, Appl. Math. Comput. 143 (2003) 1-14.
    • (2003) Appl. Math. Comput. , vol.143 , pp. 1-14
    • Climent, J.J.1    Perea, C.2
  • 9
    • 4243483806 scopus 로고    scopus 로고
    • Index of Hadamard multiplication by positive matrices II
    • G. Corach, D. Stojanoff, Index of Hadamard multiplication by positive matrices II, Linear Algebra Appl. 332-334 (2001) 503-517.
    • (2001) Linear Algebra Appl. , vol.332-334 , pp. 503-517
    • Corach, G.1    Stojanoff, D.2
  • 11
    • 0042090501 scopus 로고    scopus 로고
    • Fractional Hadamard powers of positive semidefinite matrices
    • P. Fischer, J.D. Stegeman, Fractional Hadamard powers of positive semidefinite matrices, Linear Algebra Appl. 371 (2003) 53-74.
    • (2003) Linear Algebra Appl. , vol.371 , pp. 53-74
    • Fischer, P.1    Stegeman, J.D.2
  • 12
    • 0022663313 scopus 로고
    • Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equation and the continuous Lyapunov equation
    • J. Garloff, Bounds for the eigenvalues of the solution of the discrete Riccati and Lyapunov equation and the continuous Lyapunov equation, Internat. J. Control 43 (1986) 423-431.
    • (1986) Internat. J. Control , vol.43 , pp. 423-431
    • Garloff, J.1
  • 13
    • 0018721357 scopus 로고
    • A Hessenberg-Schur method for the matrix problem AX + XB = C
    • G.H. Golub, S. Nash, C.F. Van Loan, A Hessenberg-Schur method for the matrix problem AX + XB = C, IEEE Trans. Automat. Control 24 (1979) 909-913.
    • (1979) IEEE Trans. Automat. Control , vol.24 , pp. 909-913
    • Golub, G.H.1    Nash, S.2    Van Loan, C.F.3
  • 15
    • 0015300240 scopus 로고
    • A technique for solving the extended discrete Lyapunov matrix equation
    • J. Heinen, A technique for solving the extended discrete Lyapunov matrix equation, IEEE Trans. Automat. Control 17 (1972) 156-157.
    • (1972) IEEE Trans. Automat. Control , vol.17 , pp. 156-157
    • Heinen, J.1
  • 16
    • 0026170257 scopus 로고
    • Discrete Lyapunov equation: Simultaneous eigenvalue bounds
    • A. Hmamed, Discrete Lyapunov equation: simultaneous eigenvalue bounds, Internat. J. Control 22 (1991) 1121-1126.
    • (1991) Internat. J. Control , vol.22 , pp. 1121-1126
    • Hmamed, A.1
  • 17
    • 8744269054 scopus 로고
    • The relationship between Hadamard and conventional multiplication for positive definite matrices
    • C.R. Johnson, L. Eisner, The relationship between Hadamard and conventional multiplication for positive definite matrices, Linear Algebra Appl. 92 (1987) 231-240.
    • (1987) Linear Algebra Appl. , vol.92 , pp. 231-240
    • Johnson, C.R.1    Eisner, L.2
  • 18
    • 19044380439 scopus 로고    scopus 로고
    • Recursive blocked algorithms for solving triangular systems - Part I: One-sided and coupled Sylvester-type matrix equations
    • I. Jonsson, B. Kägström, Recursive blocked algorithms for solving triangular systems - Part I: One-sided and coupled Sylvester-type matrix equations, ACM Trans. Math. Software 28 (2002) 392-415.
    • (2002) ACM Trans. Math. Software , vol.28 , pp. 392-415
    • Jonsson, I.1    Kägström, B.2
  • 19
    • 19044400922 scopus 로고    scopus 로고
    • Recursive blocked algorithms for solving triangular systems - Part II: Two-sided and generalized Sylvester and Lyapunov matrix equations
    • I. Jonsson, B. Kägström, Recursive blocked algorithms for solving triangular systems - Part II: Two-sided and generalized Sylvester and Lyapunov matrix equations, ACM Trans. Math. Software 28 (2002) 416-435.
    • (2002) ACM Trans. Math. Software , vol.28 , pp. 416-435
    • Jonsson, I.1    Kägström, B.2
  • 20
    • 21844500600 scopus 로고
    • A perturbation analysis of the generalized Sylvester equation (AR - LB, DR - LE) = (C, F)
    • B. Kägström, A perturbation analysis of the generalized Sylvester equation (AR - LB, DR - LE) = (C, F), SIAM J. Matrix Anal. Appl. 15 (1994) 1045-1060.
    • (1994) SIAM J. Matrix Anal. Appl. , vol.15 , pp. 1045-1060
    • Kägström, B.1
  • 21
    • 0023855628 scopus 로고
    • Simultaneous eigenvalue lower bounds for the Lyapunov matrix equation
    • N. Komaroff, Simultaneous eigenvalue lower bounds for the Lyapunov matrix equation, IEEE Trans. Automat. Control 33 (1988) 126-128.
    • (1988) IEEE Trans. Automat. Control , vol.33 , pp. 126-128
    • Komaroff, N.1
  • 22
    • 0026888171 scopus 로고
    • Lower bounds for the solution of the discrete algebraic Lyapunov equation
    • N. Komaroff, Lower bounds for the solution of the discrete algebraic Lyapunov equation, IEEE Trans. Automat. Control 37(1992) 1017-1019.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 1017-1019
    • Komaroff, N.1
  • 23
    • 0026885648 scopus 로고
    • Upper summation and product bounds for solution eigenvalues of the Lyapunov matrix equation
    • N. Komaroff, Upper summation and product bounds for solution eigenvalues of the Lyapunov matrix equation, IEEE Trans. Automat. Control 37 (1992) 1040-1042.
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 1040-1042
    • Komaroff, N.1
  • 24
    • 0030173646 scopus 로고    scopus 로고
    • Bounds in algebraic Riccati and Lyapunov equations: A survey and some new results
    • W.H. Kwon, Y.S. Moon, S.C. Ahn, Bounds in algebraic Riccati and Lyapunov equations: a survey and some new results, Internat. J. Control 64 (1996) 377-389.
    • (1996) Internat. J. Control , vol.64 , pp. 377-389
    • Kwon, W.H.1    Moon, Y.S.2    Ahn, S.C.3
  • 25
    • 0030244351 scopus 로고    scopus 로고
    • Upper and lower matrix bounds of the solution for the discrete Lyapunov equation
    • C.H. Lee, Upper and lower matrix bounds of the solution for the discrete Lyapunov equation, IEEE Trans. Automat. Control 41 (1996) 1338-1341.
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 1338-1341
    • Lee, C.H.1
  • 26
    • 0030144629 scopus 로고    scopus 로고
    • On the matrix bounds for the solution matrix of the discrete algebraic Riccati equation
    • C.H. Lee, On the matrix bounds for the solution matrix of the discrete algebraic Riccati equation, IEEE Trans. Circuits and Systems I 43 (1996) 402-407.
    • (1996) IEEE Trans. Circuits and Systems I , vol.43 , pp. 402-407
    • Lee, C.H.1
  • 28
    • 0021373893 scopus 로고
    • A brief summary of the bounds on the solution of the algebraic matrix equations in control theory
    • T. Mori, A. Derese, A brief summary of the bounds on the solution of the algebraic matrix equations in control theory, Internat. J. Control 39 (1984) 247-256.
    • (1984) Internat. J. Control , vol.39 , pp. 247-256
    • Mori, T.1    Derese, A.2
  • 29
    • 0036805157 scopus 로고    scopus 로고
    • On solution bounds for three types of Lyapunov matrix equations: Continuous, discrete and unified equations
    • T. Mori, H. Kokame, On solution bounds for three types of Lyapunov matrix equations: continuous, discrete and unified equations, IEEE Trans. Automat. Control 47 (2002) 1767-1770.
    • (2002) IEEE Trans. Automat. Control , vol.47 , pp. 1767-1770
    • Mori, T.1    Kokame, H.2
  • 30
    • 0029639911 scopus 로고
    • Unified type non-stationary Lyapunov matrix equation - Simultaneous eigenvalue bounds
    • M. Mrabti, M. Benseddik, Unified type non-stationary Lyapunov matrix equation - simultaneous eigenvalue bounds, Systems Control Lett. 24 (1995) 53-59.
    • (1995) Systems Control Lett. , vol.24 , pp. 53-59
    • Mrabti, M.1    Benseddik, M.2
  • 31
    • 0026715709 scopus 로고
    • Bounds for the solution of the Lyapunov matrix equation - A unified approach
    • M. Mrabti, A. Hmamed, Bounds for the solution of the Lyapunov matrix equation - a unified approach, Systems Control Lett. 18 (1992) 73-81.
    • (1992) Systems Control Lett. , vol.18 , pp. 73-81
    • Mrabti, M.1    Hmamed, A.2
  • 32
    • 0035471988 scopus 로고    scopus 로고
    • New iterative algorithm for algebraic Riccati equation related to #00 control problem of singularly perturbed systems
    • H. Mukaidani, H. Xu, K. Mizukami, New iterative algorithm for algebraic Riccati equation related to #00 control problem of singularly perturbed systems, IEEE Trans. Automat. Control 46 (2001) 1659-1666.
    • (2001) IEEE Trans. Automat. Control , vol.46 , pp. 1659-1666
    • Mukaidani, H.1    Xu, H.2    Mizukami, K.3
  • 33
    • 0742275393 scopus 로고    scopus 로고
    • ∞ control of periodic systems
    • I. Gohberg, P. Lancaster, P.N. Shivakumar (Eds.), Birkhauser, Basel, Switzerland
    • ∞ control of periodic systems, in: I. Gohberg, P. Lancaster, P.N. Shivakumar (Eds.), Recent Developments in Operator Theory and Its Applications, Birkhauser, Basel, Switzerland, 1996, pp. 263-281.
    • (1996) Recent Developments in Operator Theory and Its Applications , pp. 263-281
    • Qiu, L.1    Chen, T.2
  • 34
    • 0033100301 scopus 로고    scopus 로고
    • ∞ suboptimal controllers and the minimum entropy controller
    • ∞ suboptimal controllers and the minimum entropy controller, IEEE Trans. Automat. Control 44 (1999) 537-550.
    • (1999) IEEE Trans. Automat. Control , vol.44 , pp. 537-550
    • Qiu, L.1    Chen, T.2
  • 35
    • 0742302953 scopus 로고    scopus 로고
    • Unitary dilation approach to contractive matrix completion
    • L. Qiu, T. Chen, Unitary dilation approach to contractive matrix completion, Linear Algebra Appl. 379 (2004) 345-352.
    • (2004) Linear Algebra Appl. , vol.379 , pp. 345-352
    • Qiu, L.1    Chen, T.2
  • 37
    • 0033177761 scopus 로고    scopus 로고
    • Upper bounds for the solution of the discrete algebraic Lyapunov equation
    • M.K. Tippert, D. Marchesin, Upper bounds for the solution of the discrete algebraic Lyapunov equation, Automatica 35 (1999) 1485-1489.
    • (1999) Automatica , vol.35 , pp. 1485-1489
    • Tippert, M.K.1    Marchesin, D.2
  • 38
    • 0037720105 scopus 로고    scopus 로고
    • On an inequality for the Hadamard product of an M-matrix or an H-matrix and its inverse
    • S. Xiang, On an inequality for the Hadamard product of an M-matrix or an H-matrix and its inverse, Linear Algebra Appl. 367 (2003) 17-27.
    • (2003) Linear Algebra Appl. , vol.367 , pp. 17-27
    • Xiang, S.1


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