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Mathematical Problems in Engineering
Volume 2013, Article ID 364057, 4 pages
Research Article

Input-to-State Stability of Lur’e Hyperbolic Distributed Complex-Valued Parameter Control Systems: LOI Approach

1Institute of Dynamics and Control, School of Astronautics and Aeronautics, Tsinghua University, Beijing 100084, China
2Department of Automation, School of Information Science and Technology, Dalian Maritime University, Dalian 116026, China
3School of Industrial Engineering, Tokai University, Kumamoto 862-8652, Japan
4Department of Engineering, Faculty of Engineering and Science, University of Agder, 4898 Grimstad, Norway

Received 3 September 2012; Revised 25 December 2012; Accepted 9 January 2013

Academic Editor: Xinzhu Meng

Copyright © 2013 Zhixin Tai 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.


In this work, input-to-state stability of Lur’e hyperbolic distributed complex-valued parameter control systems has been addressed. Using comparison principle, delay-dependent sufficient conditions for the input-to-state stability in complex Hilbert spaces are established in terms of linear operator inequalities. Finally, numerical computation illustrates our result.