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Mathematical Problems in Engineering
Volume 2013, Article ID 183279, 10 pages
http://dx.doi.org/10.1155/2013/183279
Research Article

Robust Adaptive Control and Disturbance Attenuation for Uncertain Hamiltonian Systems with Time Delay

1Institute of Automation, Qufu Normal University, Qufu 273165, China
2School of Electrical Information and Automation, Qufu Normal University, Rizhao 276826, China
3Department of Automation, Southeast University, Nanjing 210096, China

Received 20 June 2013; Accepted 8 July 2013

Academic Editor: Tao Li

Copyright © 2013 Weiwei Sun et al. 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.

Abstract

This paper deals with the robust stabilizability and disturbance attenuation for a class of time-delay Hamiltonian control systems with uncertainties and external disturbances. Firstly, the robust stability of the given systems is studied, and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii (L-K) functional approach. Secondly, the problem of disturbance attenuation is considered for the Hamiltonian systems subject to external disturbances. An adaptive control law is designed corresponding to the time-varying delay pattern involved in the systems. It is shown that the closed-loop systems under the feedback control law can guarantee the γ-dissipative inequalities be satisfied. Finally, two numerical examples are provided to illustrate the theoretical developments.