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Volumn 35, Issue 7, 1990, Pages 770-776

Efficient Matrix-Valued Algorithms for Solving Stiff Riccati Differential Equations

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER PROGRAMMING--ALGORITHMS;

EID: 0025464791     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.57015     Document Type: Article
Times cited : (62)

References (20)
  • 2
    • 84976855597 scopus 로고
    • Solution of the equation AX+XB = C
    • R. H. Bartels and G. W. Stewart, “Solution of the equation AX+XB = C,” Commun. ACM, vol. 15, pp. 820-826, 1972.
    • (1972) Commun. ACM , vol.15 , pp. 820-826
    • Bartels, R.H.1    Stewart, G.W.2
  • 3
    • 70149096006 scopus 로고
    • Efficient algorithms for solving stiff matrix-valued Riccati differential equations
    • Ph.D. dissertation, ECE Dep., Univ. Calif., Santa Barbara, Sept.
    • C. H. Choi, “Efficient algorithms for solving stiff matrix-valued Riccati differential equations,” Ph.D. dissertation, ECE Dep., Univ. Calif., Santa Barbara, Sept. 1988.
    • (1988)
    • Choi, C.H.1
  • 4
    • 0023412542 scopus 로고
    • Improving the efficiency of matrix operations in the numerical solution of large implicit systems of linear differential equations
    • C. H. Choi and A. J. Laub, “Improving the efficiency of matrix operations in the numerical solution of large implicit systems of linear differential equations,” Int. J. Contr., vol. 46, pp. 991-1008, 1987.
    • (1987) Int. J. Contr. , vol.46 , pp. 991-1008
    • Choi, C.H.1    Laub, A.J.2
  • 6
    • 0015586663 scopus 로고
    • The numerical solution of the matrix Riccati differential equation
    • E. J. Davison and M. C. Maki, “The numerical solution of the matrix Riccati differential equation,” IEEE Trans. Automat. Contr., vol. AC-18, pp. 71-73, 1973.
    • (1973) IEEE Trans. Automat. Contr. , vol.AC-18 , pp. 71-73
    • Davison, E.J.1    Maki, M.C.2
  • 7
    • 0016443950 scopus 로고
    • Comparing numerical methods for stiff systems of O.D.E.'s
    • W. H. Enright, T. E. Hull, and B. Lindberg, “Comparing numerical methods for stiff systems of O.D.E.'s,” BIT, vol. 15, pp. 10-48, 1975.
    • (1975) BIT , vol.15 , pp. 10-48
    • Enright, W.H.1    Hull, T.E.2    Lindberg, B.3
  • 8
    • 0000854076 scopus 로고
    • The automatic integration of stiff ordinary differentia', equations
    • A. J. H. Morrell, Ed. Amsterdam, The Netherlands: North-Holland
    • C. W. Gear, “The automatic integration of stiff ordinary differentia', equations,” in Information Processing 68, A. J. H. Morrell, Ed. Amsterdam, The Netherlands: North-Holland, 1969, pp. 187-193.
    • (1969) Information Processing 68 , pp. 187-193
    • Gear, C.W.1
  • 10
    • 0018721357 scopus 로고
    • A Hessenberg-Schur method for the problem AX + XB = C
    • G. H. Golub, S. Nash, and C. Van Loan, “A Hessenberg-Schur method for the problem AX + XB = C,” IEEE Trans. Automat. Contr., vol. AC-24, pp. 909-913, 1979.
    • (1979) IEEE Trans. Automat. Contr. , vol.AC-24 , pp. 909-913
    • Golub, G.H.1    Nash, S.2    Van Loan, C.3
  • 11
    • 0040444397 scopus 로고
    • Bäcklund transformations for the SU‘n’ principal σ-model
    • J. Harnad, Y. Saint-Aubin, and S. Schneider, “Bäcklund transformations for the SU‘n’ principal σ-model,” J. Math. Phys., vol. 25, pp. 368-375, 1984.
    • (1984) J. Math. Phys. , vol.25 , pp. 368-375
    • Harnad, J.1    Saint-Aubin, Y.2    Schneider, S.3
  • 12
    • 36749113210 scopus 로고
    • Superposition principles for matrix Riccati equations
    • J. Harnad, P. Winternitz, and R. L. Anderson, “Superposition principles for matrix Riccati equations,” J. Math. Phys., vol. 24, pp. 1062-1072, 1983.
    • (1983) J. Math. Phys. , vol.24 , pp. 1062-1072
    • Harnad, J.1    Winternitz, P.2    Anderson, R.L.3
  • 13
    • 0020298486 scopus 로고
    • Large ordinary differential equation systems and software
    • Dec.
    • A. C. Hindmarsh, “Large ordinary differential equation systems and software,” Contr. Syst. Mag., pp. 24-30, Dec. 1981.
    • (1981) Contr. Syst. Mag. , pp. 24-30
    • Hindmarsh, A.C.1
  • 14
    • 84941478931 scopus 로고
    • COLODE: A collocation subroutine for ordinary differential equations
    • Rep. SAND74-0380, Sandia Lab., Albuquerque, NM
    • B. L. Humle, “COLODE: A collocation subroutine for ordinary differential equations,” Rep. SAND74-0380, Sandia Lab., Albuquerque, NM, 1974.
    • (1974)
    • Humle, B.L.1
  • 15
    • 84912275157 scopus 로고
    • A user's manual for the automatic synthesis program
    • June
    • R. E. Kalman and T. S. Englar, “A user's manual for the automatic synthesis program,” NASA Rep. CR-475, June 1966.
    • (1966) NASA Rep. CR-475
    • Kalman, R.E.1    Englar, T.S.2
  • 16
    • 0022132859 scopus 로고
    • Numerical integration of the differential matrix Riccati equation
    • C. S. Kenney and R. B. Leipnik, “Numerical integration of the differential matrix Riccati equation,” IEEE Trans. Automat. Contr., vol. AC-30, pp. 962-970, 1985.
    • (1985) IEEE Trans. Automat. Contr. , vol.AC-30 , pp. 962-970
    • Kenney, C.S.1    Leipnik, R.B.2
  • 17
    • 0021501125 scopus 로고
    • Applications of singular perturbation techniques to control problems
    • P. Kokotovic, “Applications of singular perturbation techniques to control problems,” SI AM Review, vol. 26, pp. 501-550, 1984.
    • (1984) SI AM Review , vol.26 , pp. 501-550
    • Kokotovic, P.1
  • 18
    • 0017009904 scopus 로고
    • Partitioned Riccati solutions and integration-free doubling algorithms
    • D. G. Lainiotis, “Partitioned Riccati solutions and integration-free doubling algorithms,” IEEE Trans. Automat. Contr., vol. AC-21, pp. 677-689, 1976.
    • (1976) IEEE Trans. Automat. Contr. , vol.AC-21 , pp. 677-689
    • Lainiotis, D.G.1
  • 19
    • 0017009729 scopus 로고
    • Generalized Chandrasekhar algorithms: Time-varying models
    • D. G. Lainiotis, “Generalized Chandrasekhar algorithms: Time-varying models,” IEEE Trans. Automat. Contr., vol. AC-21, pp. 728-732, 1976.
    • (1976) IEEE Trans. Automat. Contr. , vol.AC-21 , pp. 728-732
    • Lainiotis, D.G.1
  • 20
    • 0020258408 scopus 로고
    • Schur techniques for Riccati differential equations
    • D. Hinrichsen and A. Isidori, Eds. New York: Springer-Verlag
    • A. J. Laub, “Schur techniques for Riccati differential equations,” in Feedback Control of Linear and Nonlinear Systems, D. Hinrichsen and A. Isidori, Eds. New York: Springer-Verlag, 1982, pp. 165-174.
    • (1982) Feedback Control of Linear and Nonlinear Systems , pp. 165-174
    • Laub, A.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.