메뉴 건너뛰기




Volumn 35, Issue 1, 1997, Pages 194-204

Families of solutions of matrix riccati differential equations

Author keywords

Asymmetric Riccati differential equation; Families of solutions; Geometric characterization; Invariant subspaces; Projection preserving differential equation

Indexed keywords

CONTROL THEORY; GEOMETRY; MATRIX ALGEBRA; NUMERICAL METHODS; OPTIMAL CONTROL SYSTEMS;

EID: 0030869801     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012994276330     Document Type: Article
Times cited : (9)

References (23)
  • 1
    • 0347851738 scopus 로고
    • The testing of optimality of linear systems
    • B. D. O. ANDERSON, The testing of optimality of linear systems, Internat. J. Control, 4 (1966), pp. 29-40.
    • (1966) Internat. J. Control , vol.4 , pp. 29-40
    • Anderson, B.D.O.1
  • 2
    • 0018808291 scopus 로고
    • On the Mayne-Fraser smoothing formula and stochastic realization theory for nonstationary linear stochastic systems
    • Fort Lauderdale, FL, Dec.
    • F. BADAWI, A. LINDQUIST, AND M. PAVON, On the Mayne-Fraser smoothing formula and stochastic realization theory for nonstationary linear stochastic systems, in Proc. 18th IEEE CDC Conf., Fort Lauderdale, FL, Dec. 1979, pp. 505-510A.
    • (1979) Proc. 18th IEEE CDC Conf.
    • Badawi, F.1    Lindquist, A.2    Pavon, M.3
  • 3
    • 0038975275 scopus 로고
    • Generalized Riccati equations in dynamic games
    • S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York
    • T. BAŞAR, Generalized Riccati equations in dynamic games, in The Riccati Equation, S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York, 1989, pp. 293-333.
    • (1989) The Riccati Equation , pp. 293-333
    • Başar, T.1
  • 4
    • 0001580828 scopus 로고
    • Singular perturbation of a general boundary value problem
    • K. W. CHANG, Singular perturbation of a general boundary value problem, SIAM J. Math. Anal., 3 (1972), pp. 520-526.
    • (1972) SIAM J. Math. Anal. , vol.3 , pp. 520-526
    • Chang, K.W.1
  • 5
    • 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), pp. 179-205.
    • (1976) SIAM J. Appl. Math. , vol.31 , pp. 179-205
    • Clements, D.J.1    Anderson, B.D.O.2
  • 6
    • 84930581957 scopus 로고
    • Matrix quadratic equations
    • W. A. COPPEL, Matrix quadratic equations, Bull. Austral. Math. Soc., 10 (1974), pp. 377-401.
    • (1974) Bull. Austral. Math. Soc. , vol.10 , pp. 377-401
    • Coppel, W.A.1
  • 7
    • 0023414173 scopus 로고
    • On the existence of solutions of the Riccati differential equation
    • P. E. CROUCH AND M. PAVON, On the existence of solutions of the Riccati differential equation, Systems Control Lett., 9 (1987), pp. 203-206.
    • (1987) Systems Control Lett. , vol.9 , pp. 203-206
    • Crouch, P.E.1    Pavon, M.2
  • 8
    • 85033182085 scopus 로고    scopus 로고
    • Invariant manifolds and projective combinations of solutions of the Riccati differential equation
    • to appear
    • D. D'ALESSANDRO, Invariant manifolds and projective combinations of solutions of the Riccati differential equation, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • D'Alessandro, D.1
  • 9
    • 85033158876 scopus 로고    scopus 로고
    • A superposition theorem, for solutions of the Riccati difference equation
    • to appear
    • D. D'ALESSANDRO, A superposition theorem, for solutions of the Riccati difference equation, J. Math. Systems Estim. Control, to appear.
    • J. Math. Systems Estim. Control
    • D'Alessandro, D.1
  • 11
    • 0020089575 scopus 로고
    • A characterization of minimal square spectral factors
    • L. FINESSO AND G. PICCI, A characterization of minimal square spectral factors, IEEE Trans. Automat. Control, 27 (1982), pp. 122-127.
    • (1982) IEEE Trans. Automat. Control , vol.27 , pp. 122-127
    • Finesso, L.1    Picci, G.2
  • 12
    • 0000392569 scopus 로고
    • Nonsymmetric matrix Riccati equations
    • G. FREILING AND G. JANK, Nonsymmetric matrix Riccati equations, Z. Anal. Anwendungen, 14 (1995), pp. 259-284.
    • (1995) Z. Anal. Anwendungen , vol.14 , pp. 259-284
    • Freiling, G.1    Jank, G.2
  • 13
    • 0003132250 scopus 로고
    • Algebraic Riccati equation: Hermitian and definite solutions
    • S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York
    • V. KUČERA, Algebraic Riccati equation: Hermitian and definite solutions, in The Riccati Equation, S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York, 1989, pp. 53-88.
    • (1989) The Riccati Equation , pp. 53-88
    • Kučera, V.1
  • 14
    • 0018468516 scopus 로고
    • On the stochastic realization problem
    • A. LINDQUIST AND G. PICCI, On the stochastic realization problem, SIAM J. Control Optim., 17 (1979), pp. 365-389.
    • (1979) SIAM J. Control Optim. , vol.17 , pp. 365-389
    • Lindquist, A.1    Picci, G.2
  • 15
    • 0002992462 scopus 로고
    • Grassmannian manifolds, Riccati equations and feedback invariants of linear systems
    • C. I. Byrnes and C. F. Martin, eds., Reidel, Dordrecht, the Netherlands
    • C. F. MARTIN, Grassmannian manifolds, Riccati equations and feedback invariants of linear systems, in Geometrical Methods for the Theory of Linear Systems, C. I. Byrnes and C. F. Martin, eds., Reidel, Dordrecht, the Netherlands, 1980.
    • (1980) Geometrical Methods for the Theory of Linear Systems
    • Martin, C.F.1
  • 16
    • 0038975201 scopus 로고
    • Finite escape time for Riccati differential equations
    • C. F. MARTIN, Finite escape time for Riccati differential equations, Systems Control Letters, 1 (1981), pp. 127-131.
    • (1981) Systems Control Letters , vol.1 , pp. 127-131
    • Martin, C.F.1
  • 17
    • 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), pp. 670-677.
    • (1982) IEEE Trans. Automat. Control , vol.27 , pp. 670-677
    • Medanic, J.1
  • 18
    • 0021466124 scopus 로고
    • Optimal interpolation for linear stochastic systems
    • M. PAVON, Optimal interpolation for linear stochastic systems, SIAM J. Control Optim., 22 (1984), pp. 618-629.
    • (1984) SIAM J. Control Optim. , vol.22 , pp. 618-629
    • Pavon, M.1
  • 19
    • 0020750544 scopus 로고
    • Geometry of the algebraic Riccati equation, Parts I and II
    • M. A. SHAYMAN, Geometry of the algebraic Riccati equation, Parts I and II, SIAM J. Control Optim., 21 (1983), pp. 375-394 and pp. 395-409.
    • (1983) SIAM J. Control Optim. , vol.21 , pp. 375-394
    • Shayman, M.A.1
  • 20
    • 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), pp. 717-751.
    • (1985) SIAM J. Control Optim. , vol.23 , pp. 717-751
    • Shayman, M.A.1
  • 21
    • 0040041496 scopus 로고
    • A geometric view of the matrix Riccati equation
    • S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York
    • M. A. SHAYMAN, A geometric view of the matrix Riccati equation, in The Riccati Equation, S. Bittanti, A. Laub, and J. C. Willems, eds., Springer-Verlag, New York, 1989.
    • (1989) The Riccati Equation
    • Shayman, M.A.1
  • 22
    • 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), pp. 266-272.
    • (1985) IEEE Trans. Automat. Control , vol.30 , pp. 266-272
    • Sorine, M.1    Winternitz, P.2
  • 23
    • 0015206454 scopus 로고
    • Least squares stationary optimal control and the algebraic Riccati equation
    • J. C. WILLEMS, Least squares stationary optimal control and the algebraic Riccati equation, IEEE Trans. Automat. Control, 16 (1971), pp. 621-634.
    • (1971) IEEE Trans. Automat. Control , vol.16 , pp. 621-634
    • Willems, J.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.