Delay-Dependent Non-Fragile Robust H∞ Control for Switched Systems with Multiple Time Delays

Abstract:

The non-fragile robust H_∞ control problem is investigated for the uncertain switched discrete time systems with multiple state and input time delays. As the system and controller parameters are polytopically uncertain, the delay-dependent sufficient conditions for the existence of the non-fragile robust H_∞ controller via state feedback are presented for the systems based on the multiple Lyapunov functions and state dependent switching rules. By using the cone complementarity linearization algorithm, the nonlinear matrix inequalities relevant to the controller design can be transformed into the nonlinear programming problems constrained by the linear matrices. The simulation results show the effectiveness of the controller design method.

• Periodical: Applied Mechanics and Materials (Volumes 130-134)
• Pages: 222-226
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.130-134.222
• Online since: October 2011
• Authors: Ni Zhang, Mei Chun Fu, Tao Zou
• Keywords: H-Infinity Control, Multiple Time Delays, Non-Fragile Control, Switched System

References

[1] Y.G. Sun, L. Wang, G.M. Xie. Delay-dependent Robust Stability and Stabilization for Discrete-time Switched Systems with Mode-dependent Time-varying Delays. Applied Mathematics and Computation, 2006, 180(2): 428-435.

DOI: 10.1016/j.amc.2005.12.028

[2] L.V. Hien, Q.P. Ha, V.N. Phat. Stability and Stabilization of Switched Linear Dynamic Systems with Time Delay and Uncertainties. Applied Mathematics and Computation, 2009, 210(1): 223-231.

DOI: 10.1016/j.amc.2008.12.082

[3] Hong Nie, Ping Li, Zhengyi Song and Jun Zhao. Decentralized H∞ Robust Stability for Switched Uncertain Nonlinear Time-delay Composite Systems. Proceedings of the IEEE International Conference on Automation and Logistics, 2008, 902-907.

DOI: 10.1109/ical.2008.4636278

[4] Guangdeng Zong, Shengyuan Xu, Yuqiang Wu. Robust H∞ Stabilization for Uncertain Switched Impulsive Control Systems with State Delay: An LMI Approach. Nonlinear Analysis: Hybrid Systems, 2008, 2: 1287-1300.

DOI: 10.1016/j.nahs.2008.09.018

[5] Jie Lian, Georgi M Dimirovski. and Jun Zhao. Robust H∞ Control of Uncertain Switched Delay Systems Using Multiple Lyapunov Functions. Proceedings of the American Control Conference, Seattle, Washington, June, 2008, 1582-1587.

DOI: 10.1109/acc.2008.4586717

[6] Jie Lian, Jun Zhao, Georgi M Dimirovski. Robust H∞ Sliding Mode Control for A Class of Uncertain Switched Delay Systems. International Journal of Systems Science, 2009, 40(8): 855-866.

DOI: 10.1080/00207720902974520

[7] Yang Song, Jian Fan, Minrui Fei, Taicheng Yang. Robust H∞ Control of Discrete Switched System with Time Delay[J]. Applied Mathematics and Computation, 2008, 205(1): 159–169.

DOI: 10.1016/j.amc.2008.05.046

[8] Yijing Wang, Yao Zhenxian, Zuo Zhiqiang and Zhao Huimin. Delay-dependent Robust H∞ Control for A Class of Switched Systems with Time Delay. Proceedings of the IEEE International Symposium on Intelligent Control, San Antonio, Texas, September, 2008, 882-887.

DOI: 10.1109/wcica.2008.4593582

[9] YuanGong Sun, Long Wang, Guangming Xie. Delay-dependent Robust Stability and H∞ Control for Uncertain Discrete-time Switched Systems with Mode-dependent Time Delays. Applied Mathematics and Computation, 2007, 187(2): 1228-1237.

DOI: 10.1016/j.amc.2006.09.053

[10] L.E. Ghaoui, Oustry F. Laurent, M. AitRami. A Cone Complementarity Linearization Algorithm for Static Output-feedback and Related Problems. IEEE Transactions on Automatic Control, 1997, 42(8): 1171-1176.

DOI: 10.1109/9.618250