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Volumn 223, Issue , 2013, Pages 311-326

Computation of matrix exponentials of special matrices

Author keywords

Jordan matrix; Linear system; Matrix exponential; Similarity transformation; Special matrix; Transition matrix

Indexed keywords

LINEAR DYNAMIC SYSTEM; MATRIX EXPONENTIALS; SIMILARITY TRANSFORMATION; SPECIAL MATRICES; TRANSITION MATRICES;

EID: 84883735976     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2013.07.079     Document Type: Article
Times cited : (10)

References (42)
  • 1
    • 67349171081 scopus 로고    scopus 로고
    • Solutions to a family of matrix equations by using the Kronecker matrix polynomials
    • B. Zhou, Z.Y. Li, and G.R. Duan Solutions to a family of matrix equations by using the Kronecker matrix polynomials Applied Mathematics and Computation 212 2 2009 327 336
    • (2009) Applied Mathematics and Computation , vol.212 , Issue.2 , pp. 327-336
    • Zhou, B.1    Li, Z.Y.2    Duan, G.R.3
  • 2
    • 38949156204 scopus 로고    scopus 로고
    • Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle
    • F. Ding, P.X. Liu, and J. Ding Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle Applied Mathematics and Computation 197 1 2008 41 50
    • (2008) Applied Mathematics and Computation , vol.197 , Issue.1 , pp. 41-50
    • Ding, F.1    Liu, P.X.2    Ding, J.3
  • 3
    • 77950189548 scopus 로고    scopus 로고
    • Transformations between some special matrices
    • F. Ding Transformations between some special matrices Computers & Mathematics with Applications 59 8 2010 2676 2695
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.8 , pp. 2676-2695
    • Ding, F.1
  • 4
    • 77954174197 scopus 로고    scopus 로고
    • Computing matrix functions using mixed interpolation methods
    • M. Dehghan, and M. Hajarian Computing matrix functions using mixed interpolation methods Mathematical and Computer Modelling 52 5-6 2010 826 836
    • (2010) Mathematical and Computer Modelling , vol.52 , Issue.56 , pp. 826-836
    • Dehghan, M.1    Hajarian, M.2
  • 5
    • 79551476704 scopus 로고    scopus 로고
    • Explicit formulas for the exponentials of some special matrices
    • B.B. Wu Explicit formulas for the exponentials of some special matrices Applied Mathematics Letters 24 5 2011 642 647
    • (2011) Applied Mathematics Letters , vol.24 , Issue.5 , pp. 642-647
    • Wu, B.B.1
  • 6
    • 33749249064 scopus 로고    scopus 로고
    • 2-Norm based recursive design of transmultiplexers with designable filter length
    • Y. Shi, F. Ding, and T. Chen 2-Norm based recursive design of transmultiplexers with designable filter length Circuits, Systems and Signal Processing 25 4 2006 447 462
    • (2006) Circuits, Systems and Signal Processing , vol.25 , Issue.4 , pp. 447-462
    • Shi, Y.1    Ding, F.2    Chen, T.3
  • 7
    • 77951141155 scopus 로고    scopus 로고
    • Kalman filter based identification for systems with randomly missing measurements in a network environment
    • Y. Shi, and H. Fang Kalman filter based identification for systems with randomly missing measurements in a network environment International Journal of Control 83 3 2010 538 551
    • (2010) International Journal of Control , vol.83 , Issue.3 , pp. 538-551
    • Shi, Y.1    Fang, H.2
  • 8
    • 57249097181 scopus 로고    scopus 로고
    • Self-tuning control based on multi-innovation stochastic gradient parameter estimation
    • J.B. Zhang, F. Ding, and Y. Shi Self-tuning control based on multi-innovation stochastic gradient parameter estimation Systems & Control Letters 58 1 2009 69 75
    • (2009) Systems & Control Letters , vol.58 , Issue.1 , pp. 69-75
    • Zhang, J.B.1    Ding, F.2    Shi, Y.3
  • 9
    • 67949088087 scopus 로고    scopus 로고
    • Output feedback stabilization of networked control systems with random delays modeled by Markov chains
    • Y. Shi, and B. Yu Output feedback stabilization of networked control systems with random delays modeled by Markov chains IEEE Transactions on Automatic Control 54 7 2009 1668 1674
    • (2009) IEEE Transactions on Automatic Control , vol.54 , Issue.7 , pp. 1668-1674
    • Shi, Y.1    Yu, B.2
  • 10
    • 79955666794 scopus 로고    scopus 로고
    • Orthogonal polynomial expansions for the matrix exponential
    • G. Moore Orthogonal polynomial expansions for the matrix exponential Linear Algebra and its Applications 435 2 2011 537 559
    • (2011) Linear Algebra and Its Applications , vol.435 , Issue.2 , pp. 537-559
    • Moore, G.1
  • 11
    • 34547266552 scopus 로고    scopus 로고
    • Some new connections between matrix products for partitioned and non-partitioned matrices
    • Z. Al Zhour, and A. Kilicman Some new connections between matrix products for partitioned and non-partitioned matrices Computers & Mathematics with Applications 54 6 2007 763 784
    • (2007) Computers & Mathematics with Applications , vol.54 , Issue.6 , pp. 763-784
    • Al Zhour, Z.1    Kilicman, A.2
  • 12
    • 10444247504 scopus 로고    scopus 로고
    • Iterative least squares solutions of coupled Sylvester matrix equations
    • F. Ding, and T. Chen Iterative least squares solutions of coupled Sylvester matrix equations Systems & Control Letters 54 2 2005 95 107
    • (2005) Systems & Control Letters , vol.54 , Issue.2 , pp. 95-107
    • Ding, F.1    Chen, T.2
  • 13
    • 33751185751 scopus 로고    scopus 로고
    • On iterative solutions of general coupled matrix equations
    • F. Ding, and T. Chen On iterative solutions of general coupled matrix equations SIAM Journal on Control and Optimization 44 6 2006 2269 2284
    • (2006) SIAM Journal on Control and Optimization , vol.44 , Issue.6 , pp. 2269-2284
    • Ding, F.1    Chen, T.2
  • 14
    • 84880174907 scopus 로고    scopus 로고
    • On the Kronecker products and their applications
    • 10.1155/2013/296185 Article ID 296185
    • H.M. Zhang, and F. Ding On the Kronecker products and their applications Journal of Applied Mathematics 2013 1 8 10.1155/2013/296185 Article ID 296185
    • (2013) Journal of Applied Mathematics , pp. 1-8
    • Zhang, H.M.1    Ding, F.2
  • 15
    • 70350622178 scopus 로고    scopus 로고
    • An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices
    • M. Dehghan, and M. Hajarian An iterative method for solving the generalized coupled Sylvester matrix equations over generalized bisymmetric matrices Applied Mathematical Modelling 34 3 2010 639 654
    • (2010) Applied Mathematical Modelling , vol.34 , Issue.3 , pp. 639-654
    • Dehghan, M.1    Hajarian, M.2
  • 16
    • 79953198577 scopus 로고    scopus 로고
    • Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations
    • M. Dehghan, and M. Hajarian Analysis of an iterative algorithm to solve the generalized coupled Sylvester matrix equations Applied Mathematical Modelling 35 7 2011 3285 3300
    • (2011) Applied Mathematical Modelling , vol.35 , Issue.7 , pp. 3285-3300
    • Dehghan, M.1    Hajarian, M.2
  • 17
    • 78650265249 scopus 로고    scopus 로고
    • Bias compensation methods for stochastic systems with colored noise
    • Y. Zhang, and G.M. Cui Bias compensation methods for stochastic systems with colored noise Applied Mathematical Modelling 35 4 2011 1709 1716
    • (2011) Applied Mathematical Modelling , vol.35 , Issue.4 , pp. 1709-1716
    • Zhang, Y.1    Cui, G.M.2
  • 18
    • 79951948686 scopus 로고    scopus 로고
    • Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods
    • Y. Zhang Unbiased identification of a class of multi-input single-output systems with correlated disturbances using bias compensation methods Mathematical and Computer Modelling 53 9-10 2011 1810 1819
    • (2011) Mathematical and Computer Modelling , vol.53 , Issue.910 , pp. 1810-1819
    • Zhang, Y.1
  • 19
    • 74149086591 scopus 로고    scopus 로고
    • Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model
    • Y.J. Liu, Y.S. Xiao, and X.L. Zhao Multi-innovation stochastic gradient algorithm for multiple-input single-output systems using the auxiliary model Applied Mathematics and Computation 215 4 2009 1477 1483
    • (2009) Applied Mathematics and Computation , vol.215 , Issue.4 , pp. 1477-1483
    • Liu, Y.J.1    Xiao, Y.S.2    Zhao, X.L.3
  • 20
    • 68749087043 scopus 로고    scopus 로고
    • The residual based interactive least squares algorithms and simulation studies
    • Y.S. Xiao, Y. Zhang, J. Ding, and J.Y. Dai The residual based interactive least squares algorithms and simulation studies Computers & Mathematics with Applications 58 6 2009 1190 1197
    • (2009) Computers & Mathematics with Applications , vol.58 , Issue.6 , pp. 1190-1197
    • Xiao, Y.S.1    Zhang, Y.2    Ding, J.3    Dai, J.Y.4
  • 21
    • 64849113991 scopus 로고    scopus 로고
    • The residual based interactive stochastic gradient algorithms for controlled moving average models
    • L.Y. Wang, L. Xie, and X.F. Wang The residual based interactive stochastic gradient algorithms for controlled moving average models Applied Mathematics and Computation 211 2 2009 442 449
    • (2009) Applied Mathematics and Computation , vol.211 , Issue.2 , pp. 442-449
    • Wang, L.Y.1    Xie, L.2    Wang, X.F.3
  • 22
    • 77950187988 scopus 로고    scopus 로고
    • Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems
    • Y.J. Liu, J. Sheng, and R.F. Ding Convergence of stochastic gradient estimation algorithm for multivariable ARX-like systems Computers & Mathematics with Applications 59 8 2010 2615 2627
    • (2010) Computers & Mathematics with Applications , vol.59 , Issue.8 , pp. 2615-2627
    • Liu, Y.J.1    Sheng, J.2    Ding, R.F.3
  • 23
    • 74149087797 scopus 로고    scopus 로고
    • Time series AR modeling with missing observations based on the polynomial transformation
    • J. Ding, L.L. Han, and X.M. Chen Time series AR modeling with missing observations based on the polynomial transformation Mathematical and Computer Modelling 51 5-6 2010 527 536
    • (2010) Mathematical and Computer Modelling , vol.51 , Issue.56 , pp. 527-536
    • Ding, J.1    Han, L.L.2    Chen, X.M.3
  • 24
    • 84857030542 scopus 로고    scopus 로고
    • Iterative parameter identification methods for nonlinear functions
    • J.H. Li, R.F. Ding, and Y. Yang Iterative parameter identification methods for nonlinear functions Applied Mathematical Modelling 26 6 2012 2739 2750
    • (2012) Applied Mathematical Modelling , vol.26 , Issue.6 , pp. 2739-2750
    • Li, J.H.1    Ding, R.F.2    Yang, Y.3
  • 25
    • 33751236756 scopus 로고    scopus 로고
    • Performance analysis of multi-innovation gradient type identification methods
    • F. Ding, and T. Chen Performance analysis of multi-innovation gradient type identification methods Automatica 43 1 2007 1 14
    • (2007) Automatica , vol.43 , Issue.1 , pp. 1-14
    • Ding, F.1    Chen, T.2
  • 27
    • 67349177024 scopus 로고    scopus 로고
    • Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises
    • F. Ding, P.X. Liu, and G. Liu Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises Signal Processing 89 10 2009 1883 1890
    • (2009) Signal Processing , vol.89 , Issue.10 , pp. 1883-1890
    • Ding, F.1    Liu, P.X.2    Liu, G.3
  • 28
    • 80755182664 scopus 로고    scopus 로고
    • Bias compensation based parameter estimation for output error moving average systems
    • J. Ding, and F. Ding Bias compensation based parameter estimation for output error moving average systems International Journal of Adaptive Control and Signal Processing 25 12 2011 1100 1111
    • (2011) International Journal of Adaptive Control and Signal Processing , vol.25 , Issue.12 , pp. 1100-1111
    • Ding, J.1    Ding, F.2
  • 29
    • 84870248582 scopus 로고    scopus 로고
    • Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling
    • F. Ding Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling Applied Mathematical Modelling 37 4 2013 1694 1704
    • (2013) Applied Mathematical Modelling , vol.37 , Issue.4 , pp. 1694-1704
    • Ding, F.1
  • 30
    • 84872619148 scopus 로고    scopus 로고
    • Two-stage least squares based iterative estimation algorithm for CARARMA system modeling
    • F. Ding Two-stage least squares based iterative estimation algorithm for CARARMA system modeling Applied Mathematical Modelling 37 7 2013 4798 4808
    • (2013) Applied Mathematical Modelling , vol.37 , Issue.7 , pp. 4798-4808
    • Ding, F.1
  • 31
    • 84872587309 scopus 로고    scopus 로고
    • Decomposition based fast least squares algorithm for output error systems
    • F. Ding Decomposition based fast least squares algorithm for output error systems Signal Processing 93 5 2013 1235 1242
    • (2013) Signal Processing , vol.93 , Issue.5 , pp. 1235-1242
    • Ding, F.1
  • 32
    • 80755154802 scopus 로고    scopus 로고
    • Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems
    • J.H. Li, F. Ding, and G.W. Yang Maximum likelihood least squares identification method for input nonlinear finite impulse response moving average systems Mathematical and Computer Modelling 55 3-4 2012 442 450
    • (2012) Mathematical and Computer Modelling , vol.55 , Issue.34 , pp. 442-450
    • Li, J.H.1    Ding, F.2    Yang, G.W.3
  • 33
    • 80755164091 scopus 로고    scopus 로고
    • Maximum likelihood least squares identification for systems with autoregressive moving average noise
    • W. Wang, F. Ding, and J.Y. Dai Maximum likelihood least squares identification for systems with autoregressive moving average noise Applied Mathematical Modelling 36 5 2012 1842 1853
    • (2012) Applied Mathematical Modelling , vol.36 , Issue.5 , pp. 1842-1853
    • Wang, W.1    Ding, F.2    Dai, J.Y.3
  • 34
    • 80755175919 scopus 로고    scopus 로고
    • Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique
    • J.H. Li, and F. Ding Maximum likelihood stochastic gradient estimation for Hammerstein systems with colored noise based on the key term separation technique Computers & Mathematics with Applications 62 11 2011 4170 4177
    • (2011) Computers & Mathematics with Applications , vol.62 , Issue.11 , pp. 4170-4177
    • Li, J.H.1    Ding, F.2
  • 35
    • 78951487217 scopus 로고    scopus 로고
    • Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems
    • Z.N. Zhang, F. Ding, and X.G. Liu Hierarchical gradient based iterative parameter estimation algorithm for multivariable output error moving average systems Computers & Mathematics with Applications 61 3 2011 672 682
    • (2011) Computers & Mathematics with Applications , vol.61 , Issue.3 , pp. 672-682
    • Zhang, Z.N.1    Ding, F.2    Liu, X.G.3
  • 36
    • 77649187438 scopus 로고    scopus 로고
    • Hierarchical least squares based iterative identification for multivariable systems with moving average noises
    • H.Q. Han, and L. Xie Hierarchical least squares based iterative identification for multivariable systems with moving average noises Mathematical and Computer Modelling 51 9-10 2010 1213 1220
    • (2010) Mathematical and Computer Modelling , vol.51 , Issue.910 , pp. 1213-1220
    • Han, H.Q.1    Xie, L.2
  • 37
    • 80455150117 scopus 로고    scopus 로고
    • Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data
    • J. Ding, F. Ding, X.P. Liu, and G. Liu Hierarchical least squares identification for linear SISO systems with dual-rate sampled-data IEEE Transactions on Automatic Control 56 11 2011 2677 2683
    • (2011) IEEE Transactions on Automatic Control , vol.56 , Issue.11 , pp. 2677-2683
    • Ding, J.1    Ding, F.2    Liu, X.P.3    Liu, G.4
  • 38
    • 77955391352 scopus 로고    scopus 로고
    • Partially coupled stochastic gradient identification methods for non-uniformly sampled systems
    • F. Ding, G. Liu, and X.P. Liu Partially coupled stochastic gradient identification methods for non-uniformly sampled systems IEEE Transactions on Automatic Control 55 8 2010 1976 1981
    • (2010) IEEE Transactions on Automatic Control , vol.55 , Issue.8 , pp. 1976-1981
    • Ding, F.1    Liu, G.2    Liu, X.P.3
  • 39
    • 84875381260 scopus 로고    scopus 로고
    • Coupled-least-squares identification for multivariable systems
    • F. Ding Coupled-least-squares identification for multivariable systems IET Control Theory and Applications 7 1 2013 68 79
    • (2013) IET Control Theory and Applications , vol.7 , Issue.1 , pp. 68-79
    • Ding, F.1
  • 40
    • 79551472381 scopus 로고    scopus 로고
    • Identification methods for Hammerstein nonlinear systems
    • F. Ding, X.P. Liu, and G. Liu Identification methods for Hammerstein nonlinear systems Digital Signal Processing 21 2 2011 215 238
    • (2011) Digital Signal Processing , vol.21 , Issue.2 , pp. 215-238
    • Ding, F.1    Liu, X.P.2    Liu, G.3
  • 42
    • 84875377098 scopus 로고    scopus 로고
    • Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle
    • F. Ding, X.G. Liu, and J. Chu Gradient-based and least-squares-based iterative algorithms for Hammerstein systems using the hierarchical identification principle IET Control Theory and Applications 7 2 2013 176 184
    • (2013) IET Control Theory and Applications , vol.7 , Issue.2 , pp. 176-184
    • Ding, F.1    Liu, X.G.2    Chu, J.3


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