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Volumn 332-334, Issue , 2001, Pages 81-109

Newton's method for a rational matrix equation occurring in stochastic control

Author keywords

05C50; 15A36; 15A42; Concave operators; Matrix equations; Newton's method; Positive operators; Stochastic control

Indexed keywords


EID: 0035426962     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(00)00144-0     Document Type: Article
Times cited : (70)

References (25)
  • 1
    • 84960611544 scopus 로고
    • Resolvent positive operators
    • Arendt W. Resolvent positive operators. Proc. London Math. Soc. 54(3):1987;321-349.
    • (1987) Proc. London Math. Soc. , vol.54 , Issue.3 , pp. 321-349
    • Arendt, W.1
  • 2
    • 0038034806 scopus 로고
    • Linear equations over cones with applications to matrix theory
    • Berman A., Ben Israel A. Linear equations over cones with applications to matrix theory. Linear Algebra Appl. 7:1973;139-149.
    • (1973) Linear Algebra Appl. , vol.7 , pp. 139-149
    • Berman, A.1    Ben Israel, A.2
  • 4
    • 0016522050 scopus 로고
    • Completely positive linear maps on complex matrices
    • Choi M.-D. Completely positive linear maps on complex matrices. Linear Algebra Appl. 10:1975;285-290.
    • (1975) Linear Algebra Appl. , vol.10 , pp. 285-290
    • Choi, M.-D.1
  • 5
    • 84930581957 scopus 로고
    • Matrix quadratic equations
    • Coppel W.A. Matrix quadratic equations. Bull. Aust. Math. Soc. 10:1974;377-401.
    • (1974) Bull. Aust. Math. Soc. , vol.10 , pp. 377-401
    • Coppel, W.A.1
  • 6
    • 0025399388 scopus 로고
    • On the existence of maximal solutions for generalized algebraic Riccati equations arising in stochastic control
    • de Souza C.E., Fragoso M.D. On the existence of maximal solutions for generalized algebraic Riccati equations arising in stochastic control. Syst. Control Lett. 14:1990;233-239.
    • (1990) Syst. Control Lett. , vol.14 , pp. 233-239
    • De Souza, C.E.1    Fragoso, M.D.2
  • 8
    • 0012343959 scopus 로고    scopus 로고
    • On the disturbance attenuation problem for a wide class of time invariant linear stochastic systems
    • El Bouhtouri A., Hinrichsen D., Pritchard A.J. On the disturbance attenuation problem for a wide class of time invariant linear stochastic systems. Stochastics Stochastics Rep. 65:1999;255-297.
    • (1999) Stochastics Stochastics Rep. , vol.65 , pp. 255-297
    • El Bouhtouri, A.1    Hinrichsen, D.2    Pritchard, A.J.3
  • 10
    • 0015065214 scopus 로고
    • Optimal stationary control with state and control dependent noise
    • Haussmann U.G. Optimal stationary control with state and control dependent noise. SIAM J. Control Optim. 9:1971;713-739.
    • (1971) SIAM J. Control Optim. , vol.9 , pp. 713-739
    • Haussmann, U.G.1
  • 11
    • 0346590834 scopus 로고
    • Stabilization of linear systems with multiplicative noise
    • in: R.F. Curtain (Ed.), Springer, Berlin, July
    • U.G. Haussmann, Stabilization of linear systems with multiplicative noise. in: R.F. Curtain (Ed.), Stability of Stochastic Dynamical Systems, Lecture Notes in Mathematics, vol. 294, Springer, Berlin, July 1972, pp. 125-130.
    • (1972) Stability of Stochastic Dynamical Systems, Lecture Notes in Mathematics , vol.294 , pp. 125-130
    • Haussmann, U.G.1
  • 17
    • 0003076496 scopus 로고
    • Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems
    • Ran A.C.M., Vreugdenhil R. Existence and comparison theorems for algebraic Riccati equations for continuous- and discrete-time systems. Linear Algebra Appl. 99:1988;63-83.
    • (1988) Linear Algebra Appl. , vol.99 , pp. 63-83
    • Ran, A.C.M.1    Vreugdenhil, R.2
  • 18
    • 0642296091 scopus 로고
    • Positive operators and an inertia theorem
    • Schneider H. Positive operators and an inertia theorem. Numer. Math. 7:1968;11-17.
    • (1968) Numer. Math. , vol.7 , pp. 11-17
    • Schneider, H.1
  • 19
    • 0041353724 scopus 로고    scopus 로고
    • The discrete algebraic Riccati equation and linear matrix inequality
    • Stoorvogel A.A., Saberi A. The discrete algebraic Riccati equation and linear matrix inequality. Linear Algebra Appl. 274:1998;317-365.
    • (1998) Linear Algebra Appl. , vol.274 , pp. 317-365
    • Stoorvogel, A.A.1    Saberi, A.2
  • 20
    • 0000960420 scopus 로고
    • Spectral properties of matrices which have invariant cones
    • J.S. Vandergraft, Spectral properties of matrices which have invariant cones, SIAM J. Appl. Math. 16 (6) (1968) 1208-1222.
    • (1968) SIAM J. Appl. Math. , vol.16 , Issue.6 , pp. 1208-1222
    • Vandergraft, J.S.1
  • 21
    • 0015206454 scopus 로고
    • Least squares optimal control and the algebraic Riccati equation
    • Willems J.C. Least squares optimal control and the algebraic Riccati equation. IEEE Trans. Automat. Control. AC-16:1971;621-634.
    • (1971) IEEE Trans. Automat. Control , vol.16 , pp. 621-634
    • Willems, J.C.1
  • 22
    • 0022043995 scopus 로고
    • Monotonicity of maximal solutions of algebraic Riccati equations
    • Wimmer H.K. Monotonicity of maximal solutions of algebraic Riccati equations. Syst. Control Lett. 5:1985;317-319.
    • (1985) Syst. Control Lett. , vol.5 , pp. 317-319
    • Wimmer, H.K.1
  • 24
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • Wonham W.M. On a matrix Riccati equation of stochastic control. SIAM J. Control Optim. 6:1968;681-698.
    • (1968) SIAM J. Control Optim. , vol.6 , pp. 681-698
    • Wonham, W.M.1
  • 25
    • 0000442857 scopus 로고
    • A frequency theorem in control theory
    • Yakubovich V.A. A frequency theorem in control theory. Sib. Math. J. 14:1973;265-289.
    • (1973) Sib. Math. J. , vol.14 , pp. 265-289
    • Yakubovich, V.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.