메뉴 건너뛰기




Volumn 351-352, Issue , 2002, Pages 243-270

A survey of nonsymmetric Riccati equations

Author keywords

Algebraic Riccati equations; Applications of Riccati equations; Matrix Riccati differential equations; Properties of solutions

Indexed keywords

ALGEBRA; DIFFERENTIAL EQUATIONS; MATRIX ALGEBRA; SURVEYS;

EID: 84943618662     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00534-1     Document Type: Article
Times cited : (110)

References (105)
  • 3
    • 45449123251 scopus 로고    scopus 로고
    • An application of the decomposition method to the matrix Riccati equation in a neutron transport process
    • G. Adomian, M. Pandolfi, and R. Rach An application of the decomposition method to the matrix Riccati equation in a neutron transport process J. Math. Anal. Appl. 136 1998 557 567
    • (1998) J. Math. Anal. Appl. , vol.136 , pp. 557-567
    • Adomian, G.1    Pandolfi, M.2    Rach, R.3
  • 4
    • 0027702588 scopus 로고
    • Optimal control of weakly coupled bilinear systems
    • Z. Aganovic, and Z. Gajic Optimal control of weakly coupled bilinear systems Automatica 29 1993 1591 1593
    • (1993) Automatica , vol.29 , pp. 1591-1593
    • Aganovic, Z.1    Gajic, Z.2
  • 5
    • 0039070231 scopus 로고
    • Diffuse reflection of light by a foggy medium
    • V.A. Ambartsumian Diffuse reflection of light by a foggy medium Dokl. Akad. Nauk SSSR 38 1943 229 232
    • (1943) Dokl. Akad. Nauk SSSR , vol.38 , pp. 229-232
    • Ambartsumian, V.A.1
  • 6
    • 0041584650 scopus 로고
    • Pole placement and order reduction in two-time-scale control systems through Riccati iteration
    • L.R. Anderson Pole placement and order reduction in two-time-scale control systems through Riccati iteration Math. Modelling 3 1982 93 101
    • (1982) Math. Modelling , vol.3 , pp. 93-101
    • Anderson, L.R.1
  • 7
    • 0001659451 scopus 로고
    • Systems of ordinary differential equations with nonlinear superposition principles
    • L. Anderson, J. Harnard, and P. Winternitz Systems of ordinary differential equations with nonlinear superposition principles Physica D 4 1982 164 182
    • (1982) Physica D , vol.4 , pp. 164-182
    • Anderson, L.1    Harnard, J.2    Winternitz, P.3
  • 13
    • 0016167541 scopus 로고
    • Asymptotic solutions to the matrix Riccati equation
    • A.N. Beavers Jr., and E.D. Denman Asymptotic solutions to the matrix Riccati equation Math. Biosci. 20 1974 339 344
    • (1974) Math. Biosci. , vol.20 , pp. 339-344
    • Beavers, A.N.1    Denman, E.D.2
  • 16
    • 21344496899 scopus 로고
    • Differential equations and matrix inequalities on isospectral families
    • R. Brockett Differential equations and matrix inequalities on isospectral families Linear Algebra Appl. 203-204 1994 189 207
    • (1994) Linear Algebra Appl. , vol.203-204 , pp. 189-207
    • Brockett, R.1
  • 17
    • 38249001671 scopus 로고
    • A matrix cross ratio theorem for the Riccati equation
    • R.S. Bucy, and B.G. Williams A matrix cross ratio theorem for the Riccati equation Comput. Math. Appl. 26 1993 9 20
    • (1993) Comput. Math. Appl. , vol.26 , pp. 9-20
    • Bucy, R.S.1    Williams, B.G.2
  • 18
    • 27144514233 scopus 로고
    • Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations
    • G.J. Butler, CH.R. Johnson, and H. Wolkowicz Nonnegative solutions of a quadratic matrix equation arising from comparison theorems in ordinary differential equations SIAM J. Algebraic Discrete Methods 6 1985 47 53
    • (1985) SIAM J. Algebraic Discrete Methods , vol.6 , pp. 47-53
    • Butler, G.J.1    Johnson, C.H.R.2    Wolkowicz, H.3
  • 19
    • 0016971735 scopus 로고
    • Polynomial factorization via the Riccati equation
    • D.J. Clements, and B.D.O. Anderson Polynomial factorization via the Riccati equation SIAM J. Appl. Math. 31 1976 179 205
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 179-205
    • Clements, D.J.1    Anderson, B.D.O.2
  • 20
    • 0343360348 scopus 로고
    • Comparison theorems for canonical systems of differential equations
    • W.A. Coppel Comparison theorems for canonical systems of differential equations J. Math. Anal. Appl. 17 1965 306 315
    • (1965) J. Math. Anal. Appl. , vol.17 , pp. 306-315
    • Coppel, W.A.1
  • 21
    • 0025475531 scopus 로고
    • Comparison theorems for infinite-dimensional Riccati equations
    • R.F. Curtain, and L. Rodman Comparison theorems for infinite-dimensional Riccati equations Systems Control Lett. 15 1990 153 159
    • (1990) Systems Control Lett. , vol.15 , pp. 153-159
    • Curtain, R.F.1    Rodman, L.2
  • 22
    • 4243804546 scopus 로고    scopus 로고
    • Newton's method for a rational matrix equation occurring in stochastic control
    • Institut für dynamische Systeme, Universität Bremen
    • T. Damm, D. Hinrichsen, Newton's method for a rational matrix equation occurring in stochastic control, Report 443, Institut für dynamische Systeme, Universität Bremen, 1999
    • (1999) Report 443
    • Damm, T.1    Hinrichsen, D.2
  • 23
    • 0001464797 scopus 로고
    • Superposition formulas for rectangular matrix Riccati equations
    • M.A. del Olmo, M.A. Rodriguez, and P. Winternitz Superposition formulas for rectangular matrix Riccati equations J. Math. Phys. 28 1987 530 535
    • (1987) J. Math. Phys. , vol.28 , pp. 530-535
    • Del Olmo, M.A.1    Rodriguez, M.A.2    Winternitz, P.3
  • 24
    • 0002760220 scopus 로고
    • Total least squares and the algebraic Riccati equation
    • B. de Moor, and J. David Total least squares and the algebraic Riccati equation Systems Control Lett. 18 1992 329 337
    • (1992) Systems Control Lett. , vol.18 , pp. 329-337
    • De Moor, B.1    David, J.2
  • 25
    • 84909809133 scopus 로고
    • Generalized Riccati equations
    • C.I. Byrnes, C.F. Martin, R.E. Saeks, Elsevier Amsterdam
    • F. De Mari, and M. Shayman Generalized Riccati equations C.I. Byrnes, C.F. Martin, R.E. Saeks, Analysis and Control of Nonlinear Systems 1988 Elsevier Amsterdam 527 532
    • (1988) Analysis and Control of Nonlinear Systems , pp. 527-532
    • De Mari, F.1    Shayman, M.2
  • 26
    • 0022736868 scopus 로고
    • Invariant embedding, scattering processes and projectors in systems
    • E.D. Denman Invariant embedding, scattering processes and projectors in systems Comput. Math. Appl. Ser. A 12 1986 703 717
    • (1986) Comput. Math. Appl. Ser. A , vol.12 , pp. 703-717
    • Denman, E.D.1
  • 27
    • 36749118959 scopus 로고
    • Normal forms of elements of classical real and complex Lie and Jordan algebras
    • D.Z. Djokovic, J. Patera, P. Winternitz, and H. Zassenhaus Normal forms of elements of classical real and complex Lie and Jordan algebras J. Math. Phys. 24 1983
    • (1983) J. Math. Phys. , vol.24
    • Djokovic, D.Z.1    Patera, J.2    Winternitz, P.3    Zassenhaus, H.4
  • 28
    • 0000679502 scopus 로고    scopus 로고
    • Global solutions to a game-theoretic Riccati equation of stochastic control
    • V. Dragan, and T. Morozan Global solutions to a game-theoretic Riccati equation of stochastic control J. Differential Equations 138 1997 328 350
    • (1997) J. Differential Equations , vol.138 , pp. 328-350
    • Dragan, V.1    Morozan, T.2
  • 30
    • 84943601169 scopus 로고
    • A criterion for the matrix differential Riccati equation to be linearizable and some properties of solutions
    • M.A. Egorov A criterion for the matrix differential Riccati equation to be linearizable and some properties of solutions Differential Equations 29 1993 1461 1465
    • (1993) Differential Equations , vol.29 , pp. 1461-1465
    • Egorov, M.A.1
  • 31
    • 0343796238 scopus 로고
    • Comparison theorems and non-oscillation for differential equations in a B∗ -algebra
    • L.H. Erbe, and S. Mysore Comparison theorems and non-oscillation for differential equations in a B∗ -algebra Nonlinear Anal. 6 1982 21 33
    • (1982) Nonlinear Anal. , vol.6 , pp. 21-33
    • Erbe, L.H.1    Mysore, S.2
  • 34
    • 84943644153 scopus 로고    scopus 로고
    • Asymmetric algebraic Riccati equations: A homeomorphic parametrization of the set of solutions
    • A. Ferrante, M. Pavon, and S. Pinzone Asymmetric algebraic Riccati equations: a homeomorphic parametrization of the set of solutions Linear Algebra Appl. 329 2000 327 356
    • (2000) Linear Algebra Appl. , vol.329 , pp. 327-356
    • Ferrante, A.1    Pavon, M.2    Pinzone, S.3
  • 35
    • 0031673832 scopus 로고    scopus 로고
    • A new approach to linearly perturbed Riccati equations arising in stochastic control
    • M.D. Fragoso, O.L.V. Costa, and C.E. de Souza A new approach to linearly perturbed Riccati equations arising in stochastic control Appl. Math. Optim. 37 1998 99 126
    • (1998) Appl. Math. Optim. , vol.37 , pp. 99-126
    • Fragoso, M.D.1    Costa, O.L.V.2    De Souza, C.E.3
  • 36
    • 84943603719 scopus 로고    scopus 로고
    • Existence and convergence results for periodic Riccati differential equations
    • Karlsurhe, Germany, ECC 99
    • G. Freiling, A. Hochhaus, Existence and convergence results for periodic Riccati differential equations, in: Proceedings of European Control Conference, Karlsurhe, Germany, ECC 99, 1999
    • (1999) Proceedings of European Control Conference
    • Freiling, G.1    Hochhaus, A.2
  • 39
    • 0000392569 scopus 로고
    • Non-symmetric Riccati equations
    • G. Freiling, and G. Jank Non-symmetric Riccati equations Z. Anal. Anwendungen 14 1995 259 284
    • (1995) Z. Anal. Anwendungen , vol.14 , pp. 259-284
    • Freiling, G.1    Jank, G.2
  • 40
    • 0030264350 scopus 로고    scopus 로고
    • Existence and comparison theorems for algebraic and continuous-time Riccati differential and difference equations
    • G. Freiling, and G. Jank Existence and comparison theorems for algebraic and continuous-time Riccati differential and difference equations J. Dynamical Control Systems 2 1996 529 547
    • (1996) J. Dynamical Control Systems , vol.2 , pp. 529-547
    • Freiling, G.1    Jank, G.2
  • 41
    • 26144448264 scopus 로고    scopus 로고
    • Generalized Riccati difference and differential equations
    • G. Freiling, G. Jank, and H. Abou-Kandil Generalized Riccati difference and differential equations Linear Algebra Appl. 241-242 1996 291 303
    • (1996) Linear Algebra Appl. , vol.241-242 , pp. 291-303
    • Freiling, G.1    Jank, G.2    Abou-Kandil, H.3
  • 42
    • 0030086666 scopus 로고    scopus 로고
    • On global existence of solutions to coupled matrix Riccati equations in closed-loop Nash games
    • G. Freiling, G. Jank, and H. Abou-Kandil On global existence of solutions to coupled matrix Riccati equations in closed-loop Nash games IEEE Trans. Automat. Control 41 1996 264 269
    • (1996) IEEE Trans. Automat. Control , vol.41 , pp. 264-269
    • Freiling, G.1    Jank, G.2    Abou-Kandil, H.3
  • 43
    • 0033097606 scopus 로고    scopus 로고
    • Coupled matrix Riccati equations in minimal cost variance control problems
    • G. Freiling, G. Jank, and S.-R. Lee Coupled matrix Riccati equations in minimal cost variance control problems IEEE Trans. Automat. Control 44 1999 556 560
    • (1999) IEEE Trans. Automat. Control , vol.44 , pp. 556-560
    • Freiling, G.1    Jank, G.2    Lee, S.-R.3
  • 44
    • 0011715428 scopus 로고    scopus 로고
    • On the dependence of the solutions of algebraic and differential game Riccati equations on the parameter
    • G. Freiling, G. Jank, S.R. Lee, H. Abou-Kandil, On the dependence of the solutions of algebraic and differential game Riccati equations on the parameter μ. European J. Control 2 (1996) 69-78
    • (1996) European J. Control , vol.2 , pp. 69-78
    • Freiling, G.1    Jank, G.2    Lee, S.R.3    Abou-Kandil, H.4
  • 45
    • 85068306737 scopus 로고    scopus 로고
    • Open loop Stackelberg equilibria in linear-quadratic differential games
    • G. Freiling, G. Jank, and S.-R. Lee Open loop Stackelberg equilibria in linear-quadratic differential games J. Optim. Theory Appl. 110 2000 1 30
    • (2000) J. Optim. Theory Appl. , vol.110 , pp. 1-30
    • Freiling, G.1    Jank, G.2    Lee, S.-R.3
  • 46
    • 84994438318 scopus 로고    scopus 로고
    • Non-blow-up conditions for Riccati-type matrix differential and difference equations
    • G. Freiling, G. Jank, and A. Sarychev Non-blow-up conditions for Riccati-type matrix differential and difference equations Results Math. 37 1998 84 103
    • (1998) Results Math. , vol.37 , pp. 84-103
    • Freiling, G.1    Jank, G.2    Sarychev, A.3
  • 48
    • 0003243549 scopus 로고
    • Elements of factorization theory from a polynomial point of view. Three decades of mathematical system theory
    • Collect. Surv. Occas. 50th Birthday of Jan C. Willems
    • P.A. Fuhrmann, Elements of factorization theory from a polynomial point of view. Three decades of mathematical system theory, Collect. Surv. Occas. 50th Birthday of Jan C. Willems, Lecture Notes in Control and Information Science 135 (1989) 148-178
    • (1989) Lecture Notes in Control and Information Science , vol.135 , pp. 148-178
    • Fuhrmann, P.A.1
  • 49
    • 0001753407 scopus 로고
    • On the characterization and parametrization of minimal spectral factors
    • P.A. Fuhrmann On the characterization and parametrization of minimal spectral factors J. Math. Syst. Estim. Control 5 1995 383 444
    • (1995) J. Math. Syst. Estim. Control , vol.5 , pp. 383-444
    • Fuhrmann, P.A.1
  • 50
    • 0004050022 scopus 로고
    • Singularly perturbed and weakly coupled linear control systems. A recursive approach
    • Springer Berlin
    • Z. Gajic, D. Petkovski, and X. Shen Singularly perturbed and weakly coupled linear control systems. A recursive approach Lecture Notes in Control and Information Sciences vol. 140 1990 Springer Berlin
    • (1990) Lecture Notes in Control and Information Sciences , vol.140
    • Gajic, Z.1    Petkovski, D.2    Shen, X.3
  • 51
    • 84943614729 scopus 로고
    • Some properties of solutions of Riccati matrix differential equations
    • M. Gewert Some properties of solutions of Riccati matrix differential equations Fasc. Math. 24 1994 42 53
    • (1994) Fasc. Math. , vol.24 , pp. 42-53
    • Gewert, M.1
  • 52
    • 0026884954 scopus 로고
    • Local convergence analysis of conjugate gradient methods for solving algebraic Riccati equations
    • A.R. Ghavimi, Ch. Kenney, and A.J. Laub Local convergence analysis of conjugate gradient methods for solving algebraic Riccati equations IEEE Trans. Automat. Control 37 1992 1062 1067
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 1062-1067
    • Ghavimi, A.R.1    Kenney, Ch.2    Laub, A.J.3
  • 53
    • 0002764493 scopus 로고
    • Backward error sensitivity and refinement of computed solutions of algebraic Riccati equations
    • A.R. Ghavimi, and A.J. Laub Backward error sensitivity and refinement of computed solutions of algebraic Riccati equations Numer. Linear Algebra Appl. 2 1995 29 49
    • (1995) Numer. Linear Algebra Appl. , vol.2 , pp. 29-49
    • Ghavimi, A.R.1    Laub, A.J.2
  • 54
    • 0039837922 scopus 로고
    • Bäcklund transformations, matrix-Riccati systems and isometric immersions of space forms into space forms
    • H. Gollek Bäcklund transformations, matrix-Riccati systems and isometric immersions of space forms into space forms Colloq. Math. Soc. Janos Bolyai 56 1989 359 385
    • (1989) Colloq. Math. Soc. Janos Bolyai , vol.56 , pp. 359-385
    • Gollek, H.1
  • 55
    • 36749113210 scopus 로고
    • Superposition principles for matrix Riccati equations
    • J. Harnard, P. Winternitz, and R.L. Anderson Superposition principles for matrix Riccati equations J. Math. Phys. 24 1983 1062 1072
    • (1983) J. Math. Phys. , vol.24 , pp. 1062-1072
    • Harnard, J.1    Winternitz, P.2    Anderson, R.L.3
  • 56
    • 0026116432 scopus 로고
    • Isospectral flows on symmetric matrices and the Riccati equation
    • U. Helmke Isospectral flows on symmetric matrices and the Riccati equation Systems Control Lett. 16 1991 159 165
    • (1991) Systems Control Lett. , vol.16 , pp. 159-165
    • Helmke, U.1
  • 57
    • 0024018006 scopus 로고
    • An iterative method for the finite-time bilinear quadratic control problem
    • E. Hofer, and B. Tibken An iterative method for the finite-time bilinear quadratic control problem J. Optim. Theory Appl. 57 1988 411 427
    • (1988) J. Optim. Theory Appl. , vol.57 , pp. 411-427
    • Hofer, E.1    Tibken, B.2
  • 58
    • 84943599859 scopus 로고
    • Harmonic analysis of functions of several complex variables
    • Moscow MR, in Russian
    • H. Loo-Keng Harmonic analysis of functions of several complex variables Izdat. Inost. Lit., Moscow MR 23 1959 A3277 in Russian
    • (1959) Izdat. Inost. Lit. , vol.23 , pp. A3277
    • Loo-Keng, H.1
  • 59
    • 84910905365 scopus 로고
    • On the generalized algebraic Riccati matrix equation
    • L. Jódar, and E. Navarro On the generalized algebraic Riccati matrix equation Rev. Roumaine Math. Pures Appl. 38 1993 503 512
    • (1993) Rev. Roumaine Math. Pures Appl. , vol.38 , pp. 503-512
    • Jódar, L.1    Navarro, E.2
  • 60
    • 0039332550 scopus 로고
    • Non-autonomous Riccati-type matrix differential equations: Existence interval construction of continuous numerical solutions and error bounds
    • L. Jódar, and E. Ponsoda Non-autonomous Riccati-type matrix differential equations: existence interval construction of continuous numerical solutions and error bounds IMA J. Numer. Anal. 15 1995 61 74
    • (1995) IMA J. Numer. Anal. , vol.15 , pp. 61-74
    • Jódar, L.1    Ponsoda, E.2
  • 61
    • 44049114570 scopus 로고
    • Global existence for an abstract Riccati initial-value problem with possibly unbounded coefficients
    • J. Juang Global existence for an abstract Riccati initial-value problem with possibly unbounded coefficients J. Math. Anal. Appl. 166 1 1992 103 111
    • (1992) J. Math. Anal. Appl. , vol.166 , Issue.1 , pp. 103-111
    • Juang, J.1
  • 62
    • 21844486150 scopus 로고
    • Existence of algebraic matrix Riccati equations arising in transport theory
    • J. Juang Existence of algebraic matrix Riccati equations arising in transport theory Linear Algebra Appl. 230 1995 89 100
    • (1995) Linear Algebra Appl. , vol.230 , pp. 89-100
    • Juang, J.1
  • 63
    • 0032217347 scopus 로고    scopus 로고
    • Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices
    • J. Juang Nonsymmetric algebraic Riccati equations and Hamiltonian-like matrices SIAM J. Matrix Anal. Appl. 20 1998 228 243
    • (1998) SIAM J. Matrix Anal. Appl. , vol.20 , pp. 228-243
    • Juang, J.1
  • 64
    • 43949150679 scopus 로고
    • Comparison theorems for the matrix Riccati equation
    • J. Juang, and M.T. Lee Comparison theorems for the matrix Riccati equation Linear Algebra Appl. 196 1994 183 191
    • (1994) Linear Algebra Appl. , vol.196 , pp. 183-191
    • Juang, J.1    Lee, M.T.2
  • 65
    • 0002347639 scopus 로고
    • Solution of the Boussinesq equation on the half-line by the inverse problem
    • V.A. Jurko-Yurko Solution of the Boussinesq equation on the half-line by the inverse problem Inverse Problems 7 1991 727 738
    • (1991) Inverse Problems , vol.7 , pp. 727-738
    • Jurko-Yurko, V.A.1
  • 68
    • 3342935522 scopus 로고
    • Singular perturbations and order reduction in control theory: An overview
    • P.V. Kokotovich, R.E. O'Malley Jr., and P. Sannuti Singular perturbations and order reduction in control theory: an overview Automatica 12 1976 123 321
    • (1976) Automatica , vol.12 , pp. 123-321
    • Kokotovich, P.V.1    O'Malley, R.E.2    Sannuti, P.3
  • 69
    • 0028757840 scopus 로고
    • Positive invariance and asymptotic stability of solutions to certain Riccati equations
    • H. Kuiper Positive invariance and asymptotic stability of solutions to certain Riccati equations Dynamics Stability Systems 9 1994 331 344
    • (1994) Dynamics Stability Systems , vol.9 , pp. 331-344
    • Kuiper, H.1
  • 72
    • 84968515126 scopus 로고
    • On the matrix Riccati equation
    • J.J. Levin On the matrix Riccati equation Proc. Amer. Math. Soc. 10 1959 519 524
    • (1959) Proc. Amer. Math. Soc. , vol.10 , pp. 519-524
    • Levin, J.J.1
  • 73
    • 84921962499 scopus 로고
    • On a theorem of complete separation of a linear homogeneous system of ordinary differential equations and some properties of the separation matrix
    • N.Ya. Lyascenko On a theorem of complete separation of a linear homogeneous system of ordinary differential equations and some properties of the separation matrix Ukrain. Mat. Zh. 7 1955 403 418
    • (1955) Ukrain. Mat. Zh. , vol.7 , pp. 403-418
    • Lyascenko, N.Ya.1
  • 74
    • 0010058262 scopus 로고
    • On the matrix Riccati equation
    • K. Martensson On the matrix Riccati equation Inform. Sci. 3 1971 17 49
    • (1971) Inform. Sci. , vol.3 , pp. 17-49
    • Martensson, K.1
  • 75
    • 0020138908 scopus 로고
    • Geometric properties and invariant manifolds of the Riccati equation
    • J. Medanic Geometric properties and invariant manifolds of the Riccati equation IEEE Trans. Automat. Control 27 1982 670 677
    • (1982) IEEE Trans. Automat. Control , vol.27 , pp. 670-677
    • Medanic, J.1
  • 76
    • 0016896171 scopus 로고
    • The matrix equation AZ+B-ZCZ-ZD=0
    • H.-B. Meyer The matrix equation AZ+B-ZCZ-ZD=0 SIAM J. Appl. Math. 30 1976 136 142
    • (1976) SIAM J. Appl. Math. , vol.30 , pp. 136-142
    • Meyer, H.-B.1
  • 78
    • 0030869801 scopus 로고    scopus 로고
    • Families of solutions of matrix Riccati differential equations
    • M. Pavon, and D. d'Alessandro Families of solutions of matrix Riccati differential equations SIAM J. Control 35 1997 194 204
    • (1997) SIAM J. Control , vol.35 , pp. 194-204
    • Pavon, M.1    D'Alessandro, D.2
  • 79
    • 0000022149 scopus 로고
    • Matrix quadratic solutions
    • J.E. Potter Matrix quadratic solutions SIAM J. Appl. Math. 14 1966 496 501
    • (1966) SIAM J. Appl. Math. , vol.14 , pp. 496-501
    • Potter, J.E.1
  • 80
    • 0007228448 scopus 로고
    • Über die Oszillationstheoreme der kunjugierten Punkte beim Probleme von Lagrange
    • in German
    • J. Radon Über die Oszillationstheoreme der kunjugierten Punkte beim Probleme von Lagrange Münchener Sitzungsberichte 57 1927 243 257 in German
    • (1927) Münchener Sitzungsberichte , vol.57 , pp. 243-257
    • Radon, J.1
  • 82
    • 3343000630 scopus 로고
    • Inequalities for a matrix Riccati equation
    • R. Redheffer Inequalities for a matrix Riccati equation J. Math. Mech. 8 1959 349 367
    • (1959) J. Math. Mech. , vol.8 , pp. 349-367
    • Redheffer, R.1
  • 83
    • 84943613276 scopus 로고
    • Supplementary Note to [82]
    • R. Redheffer, J. Math. Mech. 9 (1960) 745-748 (Supplementary Note to [82])
    • (1960) J. Math. Mech. , vol.9 , pp. 745-748
    • Redheffer, R.1
  • 84
    • 84968499100 scopus 로고
    • Matrix differential equations
    • R. Redheffer Matrix differential equations Bull. Amer. Math. Soc. 81 1975 1979 485 488
    • (1979) Bull. Amer. Math. Soc. , vol.81 , Issue.1975 , pp. 485-488
    • Redheffer, R.1
  • 85
    • 0002459468 scopus 로고
    • Differential equations in operator algebras
    • R. Redheffer, P. Volkmann, Differential equations in operator algebras, Math. Ann. 239 (1979) 97-110
    • (1979) Math. Ann. , vol.239 , pp. 97-110
    • Redheffer, R.1    Volkmann, P.2
  • 86
    • 84913055792 scopus 로고
    • Properties of solutions of a Riccati matrix differential equation
    • W.T. Reid Properties of solutions of a Riccati matrix differential equation J. Math. Mech. 9 1960 749 770
    • (1960) J. Math. Mech. , vol.9 , pp. 749-770
    • Reid, W.T.1
  • 88
    • 0346492534 scopus 로고
    • On the equivalence between matrix Riccati equations and Fredholm resolvents
    • A. Schumitzky On the equivalence between matrix Riccati equations and Fredholm resolvents J. Comput. System Sci. 2 1968 76 87
    • (1968) J. Comput. System Sci. , vol.2 , pp. 76-87
    • Schumitzky, A.1
  • 89
    • 0022131292 scopus 로고
    • On the phase portrait of the matrix Riccati equation arising from the periodic control problem
    • M.A. Shayman On the phase portrait of the matrix Riccati equation arising from the periodic control problem SIAM J. Control Optim. 23 1985 717 751
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 717-751
    • Shayman, M.A.1
  • 90
    • 0040041496 scopus 로고
    • A geometric view of the matrix Riccati Equation
    • S. Bittanti, A.J. Laub, J.C. Willems, Springer New York
    • M.A. Shayman A geometric view of the matrix Riccati Equation S. Bittanti, A.J. Laub, J.C. Willems, The Riccati Equation 1991 Springer New York 89 112
    • (1991) The Riccati Equation , pp. 89-112
    • Shayman, M.A.1
  • 91
    • 0002339949 scopus 로고
    • Symplectic geometry
    • C.L. Siegel Symplectic geometry Amer. J. Math. 65 1943 1 86
    • (1943) Amer. J. Math. , vol.65 , pp. 1-86
    • Siegel, C.L.1
  • 94
    • 0022024727 scopus 로고
    • Superposition laws for solutions of differential matrix Riccati equations arising in control theory
    • M. Sorine, and P. Winternitz Superposition laws for solutions of differential matrix Riccati equations arising in control theory IEEE Trans. Automat. Control 30 1985 266 272
    • (1985) IEEE Trans. Automat. Control , vol.30 , pp. 266-272
    • Sorine, M.1    Winternitz, P.2
  • 95
    • 0039435679 scopus 로고
    • A special property of the matrix Riccati equation
    • A.N. Stokes A special property of the matrix Riccati equation Bull. Austral. Math. Soc. 10 1974 245 253
    • (1974) Bull. Austral. Math. Soc. , vol.10 , pp. 245-253
    • Stokes, A.N.1
  • 96
    • 0026925326 scopus 로고
    • Hen the exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems
    • W.Ch. Su, Z. Gajic, X.M. Shen The exact slow-fast decomposition of the algebraic Riccati equation of singularly perturbed systems. IEEE Trans. Automat. Control 37 (1992) 1456-1459
    • (1992) IEEE Trans. Automat. Control , vol.37 , pp. 1456-1459
    • Ch, W.1    Su, Z.2    Gajic, X.M.3
  • 97
    • 0026135702 scopus 로고
    • Reduced-order solution to the finite-time optimal-control problems of linear weakly coupled systems
    • W.Ch. Su, and Z. Gajic Reduced-order solution to the finite-time optimal-control problems of linear weakly coupled systems IEEE Trans. Automat. Control 36 1991 498 501
    • (1991) IEEE Trans. Automat. Control , vol.36 , pp. 498-501
    • Su, W.Ch.1    Gajic, Z.2
  • 98
    • 0022805594 scopus 로고
    • A Riccati-like equation arising in suboptimal control
    • D. Teodorescu A Riccati-like equation arising in suboptimal control Internat. J. Control 44 1986 1219 1224
    • (1986) Internat. J. Control , vol.44 , pp. 1219-1224
    • Teodorescu, D.1
  • 99
    • 0016430883 scopus 로고
    • The linear quadratic cost problem with linear state constraints and the nonsymmetric Riccati equation
    • D.D. Thompson, and R.A. Volz The linear quadratic cost problem with linear state constraints and the nonsymmetric Riccati equation SIAM J. Control 13 1975 110 145
    • (1975) SIAM J. Control , vol.13 , pp. 110-145
    • Thompson, D.D.1    Volz, R.A.2
  • 100
    • 84943622382 scopus 로고
    • A note on the matrix Riccati equations - II, Transport processes with sources
    • R. Vasudevan A note on the matrix Riccati equations - II, Transport processes with sources Utilitas Math. 3 1973 107 117
    • (1973) Utilitas Math. , vol.3 , pp. 107-117
    • Vasudevan, R.1
  • 101
    • 49949140224 scopus 로고
    • On the relation of scattering matrix, Riccati equation and boundary conditions
    • A.P. Wang On the relation of scattering matrix, Riccati equation and boundary conditions J. Math. Anal. Appl. 17 1967 238 247
    • (1967) J. Math. Anal. Appl. , vol.17 , pp. 238-247
    • Wang, A.P.1
  • 103
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • erratum: SIAM J. Control, 7 (1969) 365
    • W.M. Wonham On a matrix Riccati equation of stochastic control SIAM J. Control 6 1968 681 697 erratum: SIAM J. Control, 7 (1969) 365
    • (1968) SIAM J. Control , vol.6 , pp. 681-697
    • Wonham, W.M.1
  • 104
    • 84956139727 scopus 로고
    • The matrix Riccati differential equation and the semi-group of linear fractional transformations
    • M.Kh. Zakhar-Itkin The matrix Riccati differential equation and the semi-group of linear fractional transformations Russian Math. Surveys 78 1973 89 131
    • (1973) Russian Math. Surveys , vol.78 , pp. 89-131
    • Zakhar-Itkin, M.Kh.1
  • 105
    • 84943643692 scopus 로고    scopus 로고
    • Homogeneous spaces and the Riccati equation in calculus of variations
    • Factorial, Moscow (in Russian) [English, Springer, Berlin
    • M.I. Zelikin, Homogeneous spaces and the Riccati equation in calculus of variations, Factorial, Moscow (in Russian) [English Transl.: Control Theory and Optimization I, Springer, Berlin, 2000]
    • (2000) Transl.: Control Theory and Optimization I
    • Zelikin, M.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.