메뉴 건너뛰기




Volumn 37, Issue 1-2, 2000, Pages 84-103

Non — Blow — Up Conditions for Riccati — type Matrix Differential and Difference Equations

Author keywords

34L30; 34L40; global existence of solutions; invariant sets; Non symmetric matrix Riccati differential equations

Indexed keywords


EID: 84994438318     PISSN: 14226383     EISSN: 14209012     Source Type: Journal    
DOI: 10.1007/BF03322513     Document Type: Article
Times cited : (19)

References (44)
  • 1
    • 0027677254 scopus 로고
    • Necessary conditions for constant solutions of coupled Riccati equations in Nash games
    • H. Abou-Kandil, G. Freiling and G. Jank, Necessary conditions for constant solutions of coupled Riccati equations in Nash games, Systems and Control Letters 21 (1993), 295–306
    • (1993) Systems and Control Letters , vol.21 , pp. 295-306
    • Abou-Kandil, H.1    Freiling, G.2    Jank, G.3
  • 2
    • 0007290252 scopus 로고
    • Asymptotic behavior of Leader-Follower Control: Application to Flexible Structures
    • H. Abou-Kandil, G. Freiling and G. Jank, Asymptotic behavior of Leader-Follower Control: Application to Flexible Structures. In: Proceedings of ECC, 93, Groningen (1993), 1014–1019
    • (1993) Groningen , vol.93 , pp. 1014-1019
    • Abou-Kandil, H.1    Freiling, G.2    Jank, G.3
  • 3
    • 0028494290 scopus 로고
    • Solution and asymptotic behavior of coupled Riccati equations in jump-linear systems
    • H. Abou-Kandil, G. Freiling and G. Jank, Solution and asymptotic behavior of coupled Riccati equations in jump-linear systems, IEEE Trans. Automat. Contr., AC - 39 (1994), 1631–1636
    • (1994) IEEE Trans. Automat. Contr. , vol.AC-39 , pp. 1631-1636
    • Abou-Kandil, H.1    Freiling, G.2    Jank, G.3
  • 4
    • 0030086666 scopus 로고    scopus 로고
    • On Global Existence of Solutions to Coupled Matrix Riccati Equations in Closed Loop Nash Games IEEE Trans
    • H. Abou-Kandil, G. Freiling and G. Jank, On Global Existence of Solutions to Coupled Matrix Riccati Equations in Closed Loop Nash Games IEEE Trans. Automat. Contr., AC - 41 (1996), 264–269
    • (1996) Automat. Contr. , vol.AC-41 , pp. 264-269
    • Abou-Kandil, H.1    Freiling, G.2    Jank, G.3
  • 7
    • 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
  • 10
    • 0000679502 scopus 로고    scopus 로고
    • Global solution to game-theoretic Riccati equation of stochastic control
    • V. Dragan and R. Morozan, Global solution to game-theoretic Riccati equation of stochastic control, J. Diff. Equ. 138, (1997), 328–350
    • (1997) J. Diff. Equ. , vol.138 , pp. 328-350
    • V, D.1    R, M.2
  • 13
    • 0000392569 scopus 로고
    • Non-symmetric matrix Riccati equations
    • G. Freiling and G. Jank, Non-symmetric matrix Riccati equations, Journal Analysis Appl. 14 (1995), 259–284
    • (1995) Journal Analysis Appl. , vol.14 , pp. 259-284
    • G, F.1    G, J.2
  • 14
    • 0007221658 scopus 로고    scopus 로고
    • Sufficient conditions for the existence of open loop Nash and Stackelberg strategies
    • G. Freiling, G. Jank, S.-R. Lee and A. Sarychev, Sufficient conditions for the existence of open loop Nash and Stackelberg strategies. In: Proceedings of Controlo, 96, (1996)
    • (1996) Proceedings of Controlo, 96
    • Freiling, G.1    Jank, G.2    Lee, S.-R.3    Sarychev, A.4
  • 15
    • 84949098507 scopus 로고    scopus 로고
    • Lyapunov-type functions and invariant sets for Riccati matrix differential equations
    • Bastin, van Dooren, Eds, Brussels
    • G. Freiling, G. Jank and A. Sarychev, Lyapunov-type functions and invariant sets for Riccati matrix differential equations, Proceedings of ECC 1997, Bastin, van Dooren, Eds., Brussels, (1997)
    • (1997) Proceedings of ECC
    • Freiling, G.1    Jank, G.2    Sarychev, A.3
  • 17
    • 85053821847 scopus 로고
    • Some properties of solutions of Riccati matrix differential equations
    • M. Gewert, Some properties of solutions of Riccati matrix differential equations, Fasciculi Math. 24, (1994), 43–53
    • (1994) Fasciculi Math. , vol.24 , pp. 43-53
    • M, G.1
  • 18
    • 11144234623 scopus 로고    scopus 로고
    • Solutions of Generalized Riccati Differential Equations and their Approximation
    • N. Papamichael, St. Ruscheweyh and E. B. Saff (Eds.), World Scientific Publ
    • G. Jank, And G. Kun, Solutions of Generalized Riccati Differential Equations and their Approximation, Computational Methods in Function Theory (CMFT’97), N. Papamichael, St. Ruscheweyh and E. B. Saff (Eds.), World Scientific Publ.,(1998) 1-18
    • (1998) Computational Methods in Function Theory (CMFT’97) , pp. 1-18
    • Jank, G.1    Kun, G.2
  • 19
    • 44049123017 scopus 로고
    • Rational approximate solution and error bounds for the non-symmetric Riccati matrix differential equation
    • L. Jodar, Rational approximate solution and error bounds for the non-symmetric Riccati matrix differential equation, Appl. Math. Comp. 50, (1992), 23–31
    • (1992) Appl. Math. Comp. , vol.50 , pp. 23-31
    • L, J.1
  • 20
    • 0039332550 scopus 로고
    • Non-autonomous Riccati-type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds
    • L. Jodar and E. Ponsoda, Non-autonomous Riccati-type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds, IMA J. Numerical Anal, 15 (1995), 61–74
    • (1995) IMA J. Numerical Anal , vol.15 , pp. 61-74
    • L, J.1    E, P.2
  • 21
    • 43949150679 scopus 로고
    • Comparison theorems for the matrix Riccati equation
    • J. Juanq and M. T. Lee, Comparison theorems for the matrix Riccati equation, Lin. Alg. Appl., 196, (1994), 183–191
    • (1994) Lin. Alg. Appl. , vol.196 , pp. 183-191
    • J, J.1    M, T.2
  • 22
    • 21844486150 scopus 로고
    • Existence of algebraic matrix Riccati equations arising in transport theory
    • J. Juanq, Existence of algebraic matrix Riccati equations arising in transport theory, Lin. Alg. Appl., 230, (1995), 89–100
    • (1995) Lin. Alg. Appl. , vol.230 , pp. 89-100
    • J, J.1
  • 23
    • 58149212032 scopus 로고
    • Differential inequalities and maximum principles for second order differential equations
    • H. W. Knobloch, Differential inequalities and maximum principles for second order differential equations, Nonlinear Analysis, 25 (1995), 1003–1016
    • (1995) Nonlinear Analysis , vol.25 , pp. 1003-1016
    • H. W, K.1
  • 24
    • 85053824917 scopus 로고
    • Springer-Verlag Berlin, Heidelberg, New York, Tokio
    • H. W. Knobloch and H. Kwakernaak, Lineare Kontrolltheorie, Springer-Verlag Berlin, Heidelberg, New York, Tokio, 1985
    • (1985) Lineare Kontrolltheorie
    • H. W, K.1    H, K.2
  • 25
    • 0141702885 scopus 로고    scopus 로고
    • On Riccati matrix differential equations
    • H. W. Knobloch and M. Pohl, On Riccati matrix differential equations, Results Math. 31 (1997), 337–364
    • (1997) Results Math. , vol.31 , pp. 337-364
    • H. W, K.1    M, P.2
  • 26
    • 0028757840 scopus 로고
    • Positive invariance and asymptotic stability of solutions to certain Riccati equations
    • H.J. Kuiper, Positive invariance and asymptotic stability of solutions to certain Riccati equations, Dynamics and Stability of Systems 9 (1994), 331–344
    • (1994) Dynamics and Stability of Systems , vol.9 , pp. 331-344
    • H.J, K.1
  • 28
    • 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. Contr. AC-27 (1982), 670–677
    • (1982) IEEE Trans. Automat. Contr. , vol.AC-27 , pp. 670-677
    • J, M.1
  • 29
    • 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. Contr. 35 (1997), 194–204
    • (1997) SIAM J. Contr. , vol.35 , pp. 194-204
    • M, P.1    D, D.2
  • 30
    • 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
    • R, R.1
  • 31
    • 84943613276 scopus 로고
    • Supplementary Note to
    • R. Redheffer, Supplementary Note to [30] J. Math. Mech. 9 (1960), 745–748
    • (1960) J. Math. Mech. , vol.9 , pp. 745-748
    • R, R.1
  • 32
    • 84968499100 scopus 로고
    • Matrix differential equations
    • R. Redheffer, Matrix differential equations, Bull. Amer. Math. Soc. 81 (1975), 485–488
    • (1975) Bull. Amer. Math. Soc. , vol.81 , pp. 485-488
    • R, R.1
  • 33
    • 0002459468 scopus 로고
    • Differential equations in operator algebras
    • R. Redheffer and P. Volkmann, Differential equations in operator algebras, Math. Ann. 239 (1979), 97–110
    • (1979) Math. Ann. , vol.239 , pp. 97-110
    • R, R.1    P, V.2
  • 34
    • 0030595252 scopus 로고    scopus 로고
    • Differential equations in operator algebras II. Invariance of the order cone
    • R. Redheffer and P. Volkmann, Differential equations in operator algebras II. Invariance of the order cone, J. Diff. Equat. 130 (1996), 356–367
    • (1996) J. Diff. Equat. , vol.130 , pp. 356-367
    • R, R.1    P, V.2
  • 35
    • 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
    • W. T, R.1
  • 38
    • 0022463295 scopus 로고
    • Phase portrait of the matrix Riccati equation
    • M. A. Shayman, Phase portrait of the matrix Riccati equation, SIAM J. Contr. Opt. 24 (1986), 1–65
    • (1986) SIAM J. Contr. Opt. , vol.24 , pp. 1-65
    • M. A, S.1
  • 39
    • 0040041496 scopus 로고
    • A geometric view of the matrix Riccati equation
    • S B, A L, J. C W, (eds), Springer Verlag, Berlin
    • M. A. Shayman, A geometric view of the matrix Riccati equation, The Riccati Equation, Eds.: S. Bittanti, A. Laub and J. C. Willems, Springer Verlag, Berlin, (1991)
    • (1991) The Riccati Equation
    • M. A, S.1
  • 40
    • 0007216173 scopus 로고
    • Sampled-data Nash controls in non-zero-sum differential games
    • M. Simaan and Jr. J.B. Cruz. Sampled-data Nash controls in non-zero-sum differential games, Int J. Control 17(6): 1201–1209, 1973
    • (1973) Int J. Control , vol.17 , Issue.6 , pp. 1201-1209
    • M, S.1    Cruz, J.B.2
  • 41
    • 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. Contr. AC-30 (1985), 266–272
    • (1985) IEEE Trans. Automat. Contr. , vol.AC-30 , pp. 266-272
    • M, S.1    P, W.2
  • 43
    • 0016430883 scopus 로고
    • The linear quadratic cost problem with linear state constraints and the non symmetric Riccati equation
    • D.D. Thompson and R.A. Volz, The linear quadratic cost problem with linear state constraints and the non symmetric Riccati equation, SIAM J. Contr., 13 (1975), 110–145
    • (1975) SIAM J. Contr. , vol.13 , pp. 110-145
    • D.D, T.1    R.A, V.2
  • 44
    • 84957172527 scopus 로고
    • On the Theory of the Matrix Riccati Equation
    • M. I. Zelikin, On the Theory of the Matrix Riccati Equation, Math. USSR Sbornik, 73 (1992), 341–354
    • (1992) Math. USSR Sbornik , vol.73 , pp. 341-354
    • M. I, Z.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.