- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
The Scientific World Journal
Volume 2013 (2013), Article ID 814080, 7 pages
Lyapunov Control of Quantum Systems with Impulsive Control Fields
Department of Mathematics, Tongji University, Shanghai 200092, China
Received 10 April 2013; Accepted 26 April 2013
Academic Editors: C. Chen, D. Dong, M. Jiang, and L.-C. Wang
Copyright © 2013 Wei Yang and Jitao Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- D. D'Alessandro, Introduction to Quantum Control and Dynamics, CRC Press, New York, NY, USA, 2008.
- C. Chen, D. Dong, J. Lam, J. Chu, and T. J. Tarn, “Control design of uncertain quantum systems with fuzzy estimators,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 5, pp. 820–831, 2012.
- J. M. Coron, A. Grigoriu, C. Lefter, and G. Turinici, “Quantum control design by Lyapunov trajectory tracking for dipole and polarizability coupling,” New Journal of Physics, vol. 11, Article ID 105034, 2009.
- S. Kuang and S. Cong, “Generalized control of quantum Systems in the frame of vector treatment,” Journal of Control Theory and Applications, vol. 7, no. 4, pp. 395–399, 2009.
- X. Wang and S. G. Schirmer, “Analysis of Lyapunov method for control of quantum states,” IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2259–2270, 2010.
- R. Wu and H. Rabitz, “Control landscapes for open system quantum operations,” Journal of Physics, vol. 45, no. 48, 485303 pages, 2012.
- W. Wang, L. C. Wang, and X. X. Yi, “Lyapunov control on quantum open systems in decoherence-free subspaces,” Physical Review A, vol. 82, no. 3, Article ID 034308, 4 pages, 2010.
- X. X. Yi, X. L. Huang, C. Wu, and C. H. Oh, “Driving quantum systems into decoherence-free subspaces by Lyapunov control,” Physical Review A, vol. 80, no. 5, Article ID 052316, 5 pages, 2009.
- S. W. Zhao, H. Lin, J. T. Sun, and Z. G. Xue, “An implicit Lyapunov control for finite-dimensional closed quantum systems,” International Journal of Robust and Nonlinear Control, vol. 22, no. 11, pp. 1212–1228, 2012.
- F. Albertini and D. D'Alessandro, “Notions of controllability for bilinear multilevel quantum systems,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1399–1403, 2003.
- C. Altafini, “Controllability of quantum mechanical systems by root space decomposition of su(N),” Journal of Mathematical Physics, vol. 43, no. 5, pp. 2051–2062, 2002.
- S. G. Schirmer, H. Fu, and A. I. Solomon, “Complete controllability of quantum systems,” Physical Review A, vol. 63, no. 6, Article ID 063410, 8 pages, 2001.
- K. Beauchard, J. M. Coron, M. Mirrahimi, and P. Rouchon, “Implicit Lyapunov control of finite dimensional Schrödinger equations,” Systems & Control Letters, vol. 56, no. 5, pp. 388–395, 2007.
- S. Grivopoulos and B. Bamieh, “Lyapunov-based control of quantum systems,” in Proceedings of the 42nd IEEE Conference on Decision and Control, vol. 1–6, pp. 434–438, Maui, Hawaii, USA, December 2003.
- S. Kuang and S. Cong, “Lyapunov control methods of closed quantum systems,” Automatica, vol. 44, no. 1, pp. 98–108, 2008.
- M. Mirrahimi, P. Rouchon, and G. Turinici, “Lyapunov control of bilinear Schrödinger equations,” Automatica, vol. 41, no. 11, pp. 1987–1994, 2005.
- G. Turinici and H. Rabitz, “Quantum wavefunction controllability,” Chemical Physics, vol. 267, no. 1–3, pp. 1–9, 2001.
- D. Dong and I. R. Petersen, “Controllability of quantum systems with switching control,” International Journal of Control, vol. 84, no. 1, pp. 37–46, 2011.
- S. Zhao, H. Lin, and Z. Xue, “Switching control of closed quantum systems via the Lyapunov method,” Automatica, vol. 48, no. 8, pp. 1833–1838, 2012.
- C. Li, J. Shi, and J. Sun, “Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks,” Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 10, pp. 3099–3111, 2011.
- X. Wan and J. Sun, “Adaptive-impulsive synchronization of chaotic systems,” Mathematics and Computers in Simulation, vol. 81, no. 8, pp. 1609–1617, 2011.
- L. J. Shen, J. P. Shi, and J. T. Sun, “Complete controllability of impulsive stochastic integro-differential systems,” Automatica, vol. 46, no. 6, pp. 1068–1073, 2010.
- Z. Zhang and X. Liu, “Stability analysis and synthesis of discrete impulsive switched systems with time-varying delays and parameter uncertainty,” Circuits Systems and Signal Processing, vol. 32, no. 1, pp. 61–81, 2013.
- Y. Dong and J. Sun, “On hybrid control of a class of stochastic non-linear Markovian switching systems,” Automatica, vol. 44, no. 4, pp. 990–995, 2008.
- V. Chellaboina, S. P. Bhat, and W. M. Haddad, “An invariance principle for nonlinear hybrid and impulsive dynamical systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 53, no. 3-4, pp. 527–550, 2003.