Abstract
The problem of robust H ∞ estimation for the polytopic uncertain linear system with state delay is considered. Firstly, by introducing two auxiliary matrices a new LMI representation of H ∞ performance is presented for the linear systems with a single time-varying state delay. The proposed criterion exhibits a kind of separation between the system matrices and the positive definite Lyapunov matrices. So the vertex-dependent Lyapunov functions can be adopted, and thus a less conservative result is expected to be obtained.
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R. M. Palhares and P. L. D. Peres, “Robust H ∞ filtering design with pole constraints via linear matrix inequality,” Journal of Optimization Theory and Application, vol. 102, no. 2, pp. 713–723, Feb. 1999.
H. J. Gao and C. H. Wang, “New approaches to robust l2-linf and H ∞ filtering for uncertain discrete-time systems,” Science In China (Series F), vol. 46, no. 5, pp. 356–370, Oct. 2003.
Y. S. Lin, J. X. Qian, and S. L. Xu, “A LMI approach to robust H ∞ filtering for discrete-time systems,” Proc. of IEEE Conference on Control Application, 2003, pp. 230–233.
A. W. Pila, U. Shaked, and C. E. de Souza, “H ∞ filtering for continuous-time linear systems with delay,” IEEE Trans. Automat. Contr., vol. 44, no. 7, pp. 1412–1417, July 1999.
C. E. de Souza, R. M. Palhares, and P. L. D. Peres, “Robust H ∞ filter design for uncertain linear systems with multiple time-varying state delays,” IEEE Trans. Signal Processing, vol. 49, no. 3, pp. 569–576, Mar. 2001.
E. Fridman, U. Shaked, and L. Xie, “Robust H ∞ filtering of linear systems with time-varying delay,” IEEE Trans. on Automatic Control, vol. 48, no. 1, pp. 159–165, Jan. 2003.
C. E. de Souza, R. M. Palhares, and P. L. D. Peres, “Robust H ∞ filtering for uncertain discrete-time state-delayed systems,” IEEE Trans. on Signal Processing, vol. 49, no. 8, pp. 1696–1703, Aug. 2001.
S. Femmam, “A delay-dependent approach analysis to robust filtering,” Proc. of the Thirty-Sixth Southeastern Symposium on System Theory, pp. 389–392, 2004.
H. Gao and C. Wang, “A delay-dependent approach to robust H ∞ filtering for uncertain discrete-time state-delayed systems,” IEEE Trans. on Signal Processing, vol. 52, no. 6, pp. 1631–1640, June 2004.
E. Fridman and U. Shaked, “A new H ∞ filter design for linear time delay systems,” IEEE Trans. on Signal Processing, vol. 49, no. 11, pp. 2839–2843, Nov. 2001.
E. T. Jeung, J. H. Kim, and H. B. Pari, “H ∞ output controller design for linear systems with time-varying delayed state,” IEEE Trans. on Automatic Control, vol. 43, no. 7, pp. 971–974, July 1998.
L. H. Xie, L. L. Hu, D. Zhang, and H. S. Zhang, “Robust filtering for uncertain discrete-time: An improved LMI approach,” Proc. of the 42nd IEEE Conference On Decision and Control, Hawaii, USA, 2003, pp. 906–911.
A. G. Wu, H. F. Dong, and G. R. Duan, “Improved robust Hinf estimation for uncertain continuous-time systems,” Journal of Systems Science and Complexity, vol. 20, no. 3, pp. 362–369, Sep. 2007.
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Recommended by Editorial Board member Huanshui Zhang under the direction of Editor Young II Lee. This work was supported by the Program for Changjiang Scholars and Innovative Research Team in University.
Ai-Guo Wu was born in Gong’an County, Hubei Province on September 20, 1980. He received his B.Eng. degree in Automation in 2002, M.Eng. degree in Navigation, Guidance and Control in 2004 and Ph.D. degree in Control Science and Engineering in 2008 all from Harbin Institute of Technology. In Oct. 2008, he joined with Harbin Institute of Technology Shenzhen Graduate School as an Assistant Professor. Since Dec. 2007, he has served as a reviewer from American Mathematical Reviews. He is the author and coauthor of over 40 publications. Now his main research interests include observer design, descriptor linear systems and nonlinear control.
Jin Dong is currently an undergraduate students at the Center for Control Theory and Guidance Technology, Harbin Institute of Technology, China. His research interests include robust control and nonlinear systems.
Guang-Ren Duan received his B.Sc. degree in Applied Mathematics, and both his M.Sc. and Ph.D. degrees in Control Systems Theory. From 1989 to 1991, he was a post-doctoral researcher at Harbin Institute of Technology, where he became a professor of control systems theory in 1991. He visited the University of Hull, UK, and the University of Sheffield, UK from December 1996 to October 1998, and worked at the Queen’s University of Belfast, UK from October 1998 to October 2002. Since August 2000, he has been elected Specially Employed Professor at Harbin Institute of Technology sponsored by the Cheung Kong Scholars Program of the Chinese government. He is currently the Director of the Center for Control Theory and Guidance Technology at Harbin Institute of Technology. His main research interests include robust control, descriptor systems, missile autopilot design and magnetic bearing control. Dr. Duan is a Charted Engineer in the UK, a Senior Member of IEEE and a Fellow of IEE.
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Wu, AG., Dong, J. & Duan, GR. Robust H-infinity estimation for linear time-delay systems: An improved LMI approach. Int. J. Control Autom. Syst. 7, 668–673 (2009). https://doi.org/10.1007/s12555-009-0418-y
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DOI: https://doi.org/10.1007/s12555-009-0418-y