ICA  Vol.3 No.1 , February 2012
H Control of Uncertain Fuzzy Networked Control Systems with State Quantization
Author(s) Magdi S. Mahmoud
ABSTRACT
The problem of robust H control for uncertain discrete-time Takagi and Sugeno (T-S) fuzzy networked control systems (NCSs) is investigated in this paper subject to state quantization. By taking into consideration network induced delays and packet dropouts, an improved model of network-based control is developed. A less conservative delay-dependent stability condition for the closed NCSs is derived by employing a fuzzy Lyapunov-Krasovskii functional. Robust H fuzzy controller is constructed that guarantee asymptotic stabilization of the NCSs and expressed in LMI-based conditions. A numerical example illustrates the effectiveness of the developed technique.

Cite this paper
M. Mahmoud, "H Control of Uncertain Fuzzy Networked Control Systems with State Quantization," Intelligent Control and Automation, Vol. 3 No. 1, 2012, pp. 59-70. doi: 10.4236/ica.2012.31008.
References
[1]   T. Takagi and M. Sugeno, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Transactions on Systems, Man, and Cybernetics, Vol. 15, No. 1, 1985, pp. 116-132.

[2]   K. Tanaka, T. Ikeda and H. Wang, “Robust Stabilization of a Class of Uncertain Nonlinear Systems via Fuzzy Control: Quadratic Stabilizability, Control Theory, and Linear Matrix Inequalities,” IEEE Transactions on Fuzzy Systems, Vol. 4, No. 1, 1996, pp. 1-13. doi:10.1109/91.481840

[3]   X. Guan and C. Chen, “Delay-Dependent Guaranteed Cost Control for T-S Fuzzy Systems with Time Delays,” IEEE Transactions on Fuzzy Systems, Vol. 12, No. 2, 2004, pp. 236-249. doi:10.1109/TFUZZ.2004.825085

[4]   Y. Cao and P. Frank, “Analysis and Synthesis of Nonlinear Time-Delay systems via Fuzzy Control Approach,” IEEE Transactions on Fuzzy Systems, Vol. 8, No. 2, 2000, pp. 200211. doi:10.1109/91.842153

[5]   S. Zhou and T. Li, “Robust Stabilization for Delayed Discrete-Time Fuzzy Systems via Basis-Dependent Lyapunov-Krasovskii Function,” Fuzzy Sets and Systems, Vol. 151, No. 1, 2005, pp. 139-153. doi:10.1016/j.fss.2004.08.014

[6]   S. Xu and J. Lam, “Robust Control for Uncertain Discrete-Time-Delay Fuzzy Systems via Output Feedback Controllers,” IEEE Transactions on Fuzzy Systems, Vol. 13, No. 1, 2005, pp. 82-93. doi:10.1109/TFUZZ.2004.839661

[7]   H. J. Lee, J. B. Park and G. Chen, “Robust Fuzzy Control of Nonlinear Systems with Parametric Uncertainties,” IEEE Transactions on Fuzzy Systems, Vol. 9, No. 2, 2001, pp. 369-379. doi:10.1109/91.919258

[8]   S. Chen, W. Chang and S. Su, “Robust Static OutputFeedback Stabilization for Nonlinear Discrete-Time Systems with Time Delay via Fuzzy Control Approach,” Fuzzy Sets and Systems, Vol. 13, No. 2, 2005, pp. 263272.

[9]   Y. Cao and P. Frank, “Robust Disturbance Attenuation for a Class of Uncertain Discrete-Time Fuzzy Systems,” IEEE Transactions on Fuzzy Systems, Vol. 8, No. 4, 2000, pp. 406-415. doi:10.1109/91.868947

[10]   H. Wu, “Delay-dependent Stability Analysis and Stabilization for Discrete-Time Fuzzy Systems with State Delay: A Fuzzy Lyapunov-Krasovskii Functional Approach,” IEEE Transactions on Fuzzy Systems, Vol. 36, No. 4, 2006, pp. 954-962.

[11]   H. Gao, T. Chen and J. Lam, “A New Delay System Approach to Network-Based Control,” Automatica, Vol. 44, No. 1, 2008, pp. 39-52. doi:10.1016/j.automatica.2007.04.020

[12]   J. Wu and T. Chen, “Design of Networked Control Systems with Packet Dropouts,” IEEE Transactions on Automatic Control, Vol. 52, No. 7, 2007, pp. 1314-1319.

[13]   A. Zhang and L. Yu, “Output Feedback Stabilization of Networked Control Systems with Packet Dropouts,” IEEE Transactions on Automatic Control, Vol. 52, No. 9, 2007, pp. 1705-1710. doi:10.1109/TAC.2007.904284

[14]   L. Zhang, Y. Shi, T. Chen and B. Huang, “A New Method for Stabilization of Networked Control Systems with Random Delays,” IEEE Transactions on Automatic Control, Vol. 50, No. 8, 2005, pp. 1177-1181.

[15]   M. S. Mahmoud, “Switched Time-Delay Systems,” Springer-Verlag, New York, 2010.

[16]   E. Tian, D. Yue and C. Peng, “Quantized Output Feedback Control for Networked Control Systems,” Information Sciences, Vol. 178, 2008, pp. 2734-2749. doi:10.1016/j.ins.2008.01.019

[17]   D. Yue, C. Peng and G. Tang, “Guaranteed Cost Control of Linear Systems over Networks with State and Input Quantizations,” IET Control Theory and Application, Vol. 153, No. 6, 2006, pp. 658-664. doi:10.1049/ip-cta:20050294

[18]   P. Chen and C. Yu, “Networked Control of Linear Systems with State Quantization,” Information Sciences, Vol. 177, 2007, pp. 5763-5774. doi:10.1016/j.ins.2007.05.025

[19]   M. S. Mahmoud, “Delay-Dependent Filtering of a Class of Switched Discrete-Time State-Delay Systems,” Signal Processing, Vol. 88, No. 11, 2008, pp. 2709-2719. doi:10.1016/j.sigpro.2008.05.014

[20]   M. S. Mahmoud, A. W. Saif and P. Shi, “Stabilization of Linear Switched Delay Systems: and Methods,” Journal of Optimization Theory and Applications, Vol. 142, No. 3, 2009, pp. 583-607. doi:10.1007/s10957-009-9527-2

[21]   J. Zhang, Y. Xia and M. S. Mahmoud, “Robust Generalized and Static Output Feedback Control for Uncertain Discrete-Time Fuzzy Systems,” IET Control Theory and Applications, Vol. 3, No. 7, 2009, pp. 865-876. doi:10.1049/iet-cta.2008.0146

[22]   H. Gao, P. Shi and J. Wang, “Parameter-Dependent Robust Stability of Uncertain Time-Delay Systems,” Computational & Applied Mathematics, Vol. 206, No. 1, 2007, pp. 366-373. doi:10.1016/j.cam.2006.07.027

[23]   H. Gao, J. Lam, C. Wang and Y. Wang, “Delay-Dependent Output-Feedback Stabilization of Discrete-Time Systems with Time-Varying State Delay,” IEE Proceedings of Control Theory and Applications, Vol. 151, No. 6, 2004, pp. 691-698. doi:10.1049/ip-cta:20040822

[24]   H. Gao and T. Chen, “A New Approach to Quantized Feedback Control Systems,” Automatica, Vol. 44, No. 2, 2008, pp. 534-542. doi:10.1016/j.automatica.2007.06.015

[25]   G. Walsh and H. Ye, “Scheduling of Networked Control Systems,” IEEE Control Systems Magazine, Vol. 21, No. 1, 2001, pp. 57-65. doi:10.1109/37.898792

[26]   H. Zhang, D. Yang and T. Chai, “Guaranteed Cost Networked Control for T-S Fuzzy Systems with Time Delays,” Applications and Reviews, Vol. 37, No. 2, 2007, pp. 160-172.

[27]   L. Zhang and H. Fang, “Fuzzy Controller Design for Networked Control System with Time-Variant Delays,” Journal of Systems Engineering and Electronics, Vol. 17, No. 1, 2006, pp. 172-176. doi:10.1016/S1004-4132(06)60030-3

[28]   X. Jiang and Q. Han, “On Designing Fuzzy Controllers for a Class of Nonlinear Networked Control Systems,” IEEE Transactions on Fuzzy Systems, Vol. 16, No. 4, 2008, pp. 1050-1060. doi:10.1109/TFUZZ.2008.917293

 
 
Top