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Volumn 52, Issue 11, 2007, Pages 2019-2028

Feedback stabilization of isospectral control systems on complex flag manifolds: Application to quantum ensembles

Author keywords

Bilinear control systems; Control systems; Convergence; Convergence analysis; Eigenvalues and eigenfunctions; Equations; Feedback stabilization; Manifolds; Matrix decomposition; Quantum control; Quantum mechanics

Indexed keywords

CLOSED LOOP SYSTEMS; CONTROL SYSTEM STABILITY; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; QUANTUM THEORY; STATE FEEDBACK;

EID: 38149021375     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.908306     Document Type: Article
Times cited : (71)

References (42)
  • 2
    • 0035981789 scopus 로고    scopus 로고
    • Controllability of quantum mechanical systems by root space decomposition of su(N)
    • C. Altafini, "Controllability of quantum mechanical systems by root space decomposition of su(N)," J. Math. Phys., vol. 43, no. 5, pp. 2051-2062, 2002.
    • (2002) J. Math. Phys , vol.43 , Issue.5 , pp. 2051-2062
    • Altafini, C.1
  • 3
    • 33846585369 scopus 로고    scopus 로고
    • Feedback control of spin systems
    • C. Altafini, "Feedback control of spin systems," Quantum Inf. Process., vol. 6, pp. 9-36, 2007.
    • (2007) Quantum Inf. Process , vol.6 , pp. 9-36
    • Altafini, C.1
  • 5
    • 0029208217 scopus 로고
    • Stabilizability of closed orbits
    • A. Bacciotti and L. Mazzi, "Stabilizability of closed orbits," Syst. Control Lett., vol. 24, pp. 97-101, 1995.
    • (1995) Syst. Control Lett , vol.24 , pp. 97-101
    • Bacciotti, A.1    Mazzi, L.2
  • 7
    • 0346676588 scopus 로고    scopus 로고
    • A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon
    • S. P. Bhat and D. S. Bernstein, "A topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon," Syst. Control Lett., vol. 39, no. 1, pp. 63-70, 2000.
    • (2000) Syst. Control Lett , vol.39 , Issue.1 , pp. 63-70
    • Bhat, S.P.1    Bernstein, D.S.2
  • 8
    • 12844252459 scopus 로고    scopus 로고
    • Resonance of minimizers for n-level quantum systems with an arbitrary cost
    • U. Boscain and G. Charlot, "Resonance of minimizers for n-level quantum systems with an arbitrary cost," ESAIM Control Optim. Calc. Var., vol. 10, no. 4, pp. 593-614, 2004.
    • (2004) ESAIM Control Optim. Calc. Var , vol.10 , Issue.4 , pp. 593-614
    • Boscain, U.1    Charlot, G.2
  • 9
    • 0009531307 scopus 로고    scopus 로고
    • Density matrices and geometric phases for n-state systems
    • Preprint arXiv:qUant-ph/9810084
    • L. J. Boya, M. Byrd, M. Mims, and E. C. G. Sudarshan, "Density matrices and geometric phases for n-state systems," Preprint arXiv:qUant-ph/9810084 1998.
    • (1998)
    • Boya, L.J.1    Byrd, M.2    Mims, M.3    Sudarshan, E.C.G.4
  • 10
    • 0036261831 scopus 로고    scopus 로고
    • Some mathematical and algorithmic challenges in the control of quantum dynamics phenomena
    • E. Brown and H. Rabitz, "Some mathematical and algorithmic challenges in the control of quantum dynamics phenomena," J. Math. Chem., vol. 31, pp. 17-63, 2002.
    • (2002) J. Math. Chem , vol.31 , pp. 17-63
    • Brown, E.1    Rabitz, H.2
  • 15
    • 0035365364 scopus 로고    scopus 로고
    • Optimal control of two-level quantum systems
    • Jun
    • D. D'Alessandro and M. Dahleh, "Optimal control of two-level quantum systems," IEEE Trans. Autom. Control, vol. 46, no. 6, pp. 866-876, Jun. 2001.
    • (2001) IEEE Trans. Autom. Control , vol.46 , Issue.6 , pp. 866-876
    • D'Alessandro, D.1    Dahleh, M.2
  • 16
    • 0035924746 scopus 로고    scopus 로고
    • Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach
    • E. Ercolessi, G. Marmo, and G. Morandi, "Geometry of mixed states and degeneracy structure of geometric phases for multi-level quantum systems. A unitary group approach," Int. J. Mod. Phys. A, vol. 16, pp. 5007-5032, 2001.
    • (2001) Int. J. Mod. Phys. A , vol.16 , pp. 5007-5032
    • Ercolessi, E.1    Marmo, G.2    Morandi, G.3
  • 17
    • 0036993410 scopus 로고    scopus 로고
    • Driving the propagator of a spin system: A feedback approach
    • Las Vegas, NV, Dec
    • A. Ferrante, M. Pavon, and G. Raccanelli, "Driving the propagator of a spin system: A feedback approach," in Proc. 41st Conf. Decision Control, Las Vegas, NV, Dec. 2002, pp. 46-50.
    • (2002) Proc. 41st Conf. Decision Control , pp. 46-50
    • Ferrante, A.1    Pavon, M.2    Raccanelli, G.3
  • 20
    • 1542359111 scopus 로고    scopus 로고
    • Lyapunov-based control of quantum systems
    • Maui, HI, Dec
    • S. Grivopoulos and B. Bamieh, "Lyapunov-based control of quantum systems," in Proc. 41st Conf. Decision Control, Maui, HI, Dec. 2004, pp. 434-438.
    • (2004) Proc. 41st Conf. Decision Control , pp. 434-438
    • Grivopoulos, S.1    Bamieh, B.2
  • 22
    • 0019599744 scopus 로고
    • Stabilizing controllers for bilinear systems
    • Apr
    • P. Gutman, "Stabilizing controllers for bilinear systems," IEEE Trans. Autom. Control, vol. AC-26, no. 4, pp. 917-922, Apr. 1981.
    • (1981) IEEE Trans. Autom. Control , vol.AC-26 , Issue.4 , pp. 917-922
    • Gutman, P.1
  • 24
    • 0001374626 scopus 로고
    • Controllability and stability
    • V. Jurdjevic and J. P. Quinn, "Controllability and stability," J. Differ. Equ., vol. 28, pp. 381-389, 1978.
    • (1978) J. Differ. Equ , vol.28 , pp. 381-389
    • Jurdjevic, V.1    Quinn, J.P.2
  • 25
    • 0042162967 scopus 로고    scopus 로고
    • The Bloch vector for N-level systems
    • G. Kimura, "The Bloch vector for N-level systems," Phys. Lett. A vol. 314, p. 339, 2003.
    • (2003) Phys. Lett. A , vol.314 , pp. 339
    • Kimura, G.1
  • 26
    • 0001232269 scopus 로고
    • The application of total energy as a Lyapunov function for mechanical control systems
    • Dynamics and Control of Multibody Systems, J. E. Marsden, P. S. Krishnaprasad, and J. C. Simo, Eds. Providence, RI: American Mathematical Society
    • D. E. Koditschek, "The application of total energy as a Lyapunov function for mechanical control systems," in Dynamics and Control of Multibody Systems, Contemporary Mathematics, 97, J. E. Marsden, P. S. Krishnaprasad, and J. C. Simo, Eds. Providence, RI: American Mathematical Society, 1989.
    • (1989) Contemporary Mathematics , vol.97
    • Koditschek, D.E.1
  • 27
    • 24944551258 scopus 로고    scopus 로고
    • Lyapunov control of bilinear Schrödinger equations
    • M. Mirrahimi, P. Rouchon, and G. Turinici, "Lyapunov control of bilinear Schrödinger equations," Automatica, vol. 41, pp. 1987-1994, 2005.
    • (2005) Automatica , vol.41 , pp. 1987-1994
    • Mirrahimi, M.1    Rouchon, P.2    Turinici, G.3
  • 31
    • 0000311905 scopus 로고
    • The Duistermaat-Heckman integration formula on flag manifolds
    • R. F. Picken, "The Duistermaat-Heckman integration formula on flag manifolds," J. Math. Phys., vol. 31, no. 3, pp. 616-638, 1990.
    • (1990) J. Math. Phys , vol.31 , Issue.3 , pp. 616-638
    • Picken, R.F.1
  • 32
    • 0000812871 scopus 로고    scopus 로고
    • Spheres in Hermitian symmetric spaces and flag manifolds
    • C. U. Sánchez, A. L. Calí, and J. L. Moreschi, "Spheres in Hermitian symmetric spaces and flag manifolds," Geom. Dedicata, vol. 64, no. 3, pp. 261-276, 1997.
    • (1997) Geom. Dedicata , vol.64 , Issue.3 , pp. 261-276
    • Sánchez, C.U.1    Calí, A.L.2    Moreschi, J.L.3
  • 34
    • 0042379950 scopus 로고    scopus 로고
    • Constructive control of quantum systems using factorization of unitary operators
    • S. G. Schirmer, A.D. Greentree, V. Ramakrishna, and H. Rabitz, "Constructive control of quantum systems using factorization of unitary operators," J. Phys. A, vol. 35, pp. 8315-8339, 2002.
    • (2002) J. Phys. A , vol.35 , pp. 8315-8339
    • Schirmer, S.G.1    Greentree, A.D.2    Ramakrishna, V.3    Rabitz, H.4
  • 35
    • 0842329034 scopus 로고    scopus 로고
    • Orbits of quantum states and geometry of Bloch vectors for N-level systems
    • S. G. Schirmer, T. Zhang, and J. V. Leahy, "Orbits of quantum states and geometry of Bloch vectors for N-level systems," J. Phys. A, vol. 37, pp. 1389-1402, 2004.
    • (2004) J. Phys. A , vol.37 , pp. 1389-1402
    • Schirmer, S.G.1    Zhang, T.2    Leahy, J.V.3
  • 36
    • 0035371423 scopus 로고    scopus 로고
    • Quantum wave function controllability
    • G. Turinici and H. Rabitz, "Quantum wave function controllability," Chem. Phys., vol. 267, pp. 1-9, 2001.
    • (2001) Chem. Phys , vol.267 , pp. 1-9
    • Turinici, G.1    Rabitz, H.2
  • 37
    • 21344462807 scopus 로고    scopus 로고
    • Feedback control of quantum state reduction
    • Jun
    • R. van Handel, J. K. Stockton, and H. Mabuchi, "Feedback control of quantum state reduction," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 768-780, Jun. 2005.
    • (2005) IEEE Trans. Autom. Control , vol.50 , Issue.6 , pp. 768-780
    • van Handel, R.1    Stockton, J.K.2    Mabuchi, H.3
  • 38
    • 24944484094 scopus 로고    scopus 로고
    • On the convergence of a feedback control strategy for multilevel quantum systems
    • Perpignan, France
    • P. Vettori, "On the convergence of a feedback control strategy for multilevel quantum systems," in MTNS Mathematical Theory of Networks and Systems, Perpignan, France, 2002.
    • (2002) MTNS Mathematical Theory of Networks and Systems
    • Vettori, P.1
  • 40
    • 0000716368 scopus 로고
    • The structure of the level surfaces of a Lyapunov function
    • F. W.Wilson, "The structure of the level surfaces of a Lyapunov function," J. Differ. Equ., vol. 3, pp. 323-329, 1967.
    • (1967) J. Differ. Equ , vol.3 , pp. 323-329
    • Wilson, F.W.1
  • 41
    • 0033593168 scopus 로고    scopus 로고
    • Managing dynamical singular behavior in the tracking control of quantum observables
    • W. Zhu, M. Smit, and H. Rabitz, "Managing dynamical singular behavior in the tracking control of quantum observables," J. Chem. Phys., vol. 110, pp. 1905-1915, 1999.
    • (1999) J. Chem. Phys , vol.110 , pp. 1905-1915
    • Zhu, W.1    Smit, M.2    Rabitz, H.3
  • 42
    • 0035979978 scopus 로고    scopus 로고
    • Monge metric on the sphere and geometry of quantum states
    • K. Zyczkowski and W. Slomczyński, "Monge metric on the sphere and geometry of quantum states," J. Phys. A, vol. 34, p. 6689, 2000.
    • (2000) J. Phys. A , vol.34 , pp. 6689
    • Zyczkowski, K.1    Slomczyński, W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.