H_{∞} Control of Uncertain Fuzzy Networked Control Systems with State Quantization

Author(s)
Magdi S. Mahmoud

Affiliation(s)

Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

Systems Engineering Department, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

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.

The problem of robust H

KEYWORDS

Networked H_{∞} Control; Fuzzy Systems; Discrete Time-Varying Delay; Linear Matrix Inequality (LMI)

Networked H

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.

M. Mahmoud, "H

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

[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