L 2 disturbance attenuation for a class of time-delay Hamiltonian systems

Authors

Abstract

This paper considers the problem of L _2-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ -dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L _2 disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.

Keywords

disturbance attenuation, hamiltonian systems, stability, time-delay

Citation

Journal: Journal of Systems Science and Complexity
Year: 2011
Volume: 24
Issue: 4
Pages: 672–682
Publisher: Springer Science and Business Media LLC
DOI: 10.1007/s11424-011-8368-x

BibTeX

@article{Sun_2011,
  title={{L 2 disturbance attenuation for a class of time-delay Hamiltonian systems}},
  volume={24},
  ISSN={1559-7067},
  DOI={10.1007/s11424-011-8368-x},
  number={4},
  journal={Journal of Systems Science and Complexity},
  publisher={Springer Science and Business Media LLC},
  author={Sun, Weiwei and Wang, Yuzhen and Yang, Renming},
  year={2011},
  pages={672--682}
}

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References

Isidori, A. Nonlinear Control Systems II. Communications and Control Engineering (Springer London, 1999). doi:10.1007/978-1-4471-0549-7 – 10.1007/978-1-4471-0549-7
van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes 25, 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
D. Cheng, Journal of Systems Science & Complexity (2002)
Cheng, D. & Guo, Y. Stabilization of nonlinear systems via the center manifold approach. Systems & Control Letters 57, 511–518 (2008) – 10.1016/j.sysconle.2006.10.029
Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
Yuzhen Wang, Daizhan Cheng, Chunwen Li & You Ge. Dissipative hamiltonian realization and energy-based L/sub 2/-disturbance attenuation control of multimachine power systems. IEEE Trans. Automat. Contr. 48, 1428–1433 (2003) – 10.1109/tac.2003.815037
Wang, Y., Feng, G. & Cheng, D. Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems. Automatica 43, 403–415 (2007) – 10.1016/j.automatica.2006.09.008
Xi, Z., Cheng, D., Lu, Q. & Mei, S. Nonlinear decentralized controller design for multimachine power systems using Hamiltonian function method. Automatica 38, 527–534 (2002) – 10.1016/s0005-1098(01)00233-3
Xi, Z. & Lam, J. Stabilization of generalized Hamiltonian systems with internally generated energy and applications to power systems. Nonlinear Analysis: Real World Applications 9, 1202–1223 (2008) – 10.1016/j.nonrwa.2007.02.015
Shen, T., Ortega, R., Lu, Q., Mei, S. & Tamura, K. Adaptive L/sub 2/ disturbance attenuation of Hamiltonian systems with parametric perturbation and application to power systems. Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187) vol. 5 4939–4944 – 10.1109/cdc.2001.914715
Wang, Y., Feng, G., Cheng, D. & Liu, Y. Adaptive \(L_{2}\) disturbance attenuation control of multi-machine power systems with SMES units. Automatica 42, 1121–1132 (2006) – 10.1016/j.automatica.2006.03.014
Gu, K., Kharitonov, V. L. & Chen, J. Stability of Time-Delay Systems. (Birkhäuser Boston, 2003). doi:10.1007/978-1-4612-0039-0 – 10.1007/978-1-4612-0039-0
Lin, Z. & Fang, H. On Asymptotic Stabilizability of Linear Systems With Delayed Input. IEEE Trans. Automat. Contr. 52, 998–1013 (2007) – 10.1109/tac.2007.899007
Mazenc, F. & Niculescu, S.-I. Lyapunov stability analysis for nonlinear delay systems. Systems & Control Letters 42, 245–251 (2001) – 10.1016/s0167-6911(00)00093-1
Qu, J. & Gao, C. Stability Analysis for the Large-Scale Systems with Time-Delay. Jrl Syst Sci & Complex 19, 558–565 (2006) – 10.1007/s11424-006-0558-6
Wu, M., He, Y., She, J.-H. & Liu, G.-P. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica 40, 1435–1439 (2004) – 10.1016/j.automatica.2004.03.004
Xu, S., Lam, J. & Zou, Y. New results on delay-dependent robust \(H_{\infty}\) control for systems with time-varying delays. Automatica 42, 343–348 (2006) – 10.1016/j.automatica.2005.09.013
Yue, D., Han, Q.-L. & Lam, J. Network-based robust \(H_{\infty}\) control of systems with uncertainty. Automatica 41, 999–1007 (2005) – 10.1016/j.automatica.2004.12.011
Sun, W., Wang, Y. & Feng, G. Stability Analysis for Time-Delay Hamiltonian Systems. 2006 9th International Conference on Control, Automation, Robotics and Vision 1–6 (2006) doi:10.1109/icarcv.2006.345259 – 10.1109/icarcv.2006.345259
J. Slotine, Applied Nonlinear Control (1991)