Browse > Article
http://dx.doi.org/10.5370/KIEE.2016.65.9.1524

Robust ℋ∞ Sampled-Data Control for Takagi-Sugeno Fuzzy Model with Singular Perturbation  

Kang, Hyoung Bin (Dept. of Electronic Engineering, Inha University)
Moon, Ji Hyun (Dept. of Electronic Engineering, Inha University)
Lee, Ho Jae (Dept. of Electronic Engineering, Inha University)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.65, no.9, 2016 , pp. 1524-1530 More about this Journal
Abstract
This paper deals with a robust $H_{\infty}$ sampled-data controller design problem for nonlinear systems in Takagi-Sugeno fuzzy form with singular perturbation. The employed controller takes a state-feedback form. The design condition is represented in terms of linear matrix inequalities. A numerical examples is included to show the effectiveness of the theoretical development.
Keywords
Takagi-Sugeno fuzzy model; singular perturbation; $H_{\infty}$ sampled-data control; state feedback;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 H. K. Lam, H. Li, C. Deters, E. L. Secco, H. A. Wurdemann, and K. Althoefer, "Control design for interval type-2 fuzzy systems under imperfect premise matching," IEEE Trans. Ind. Electron., vol. 61, pp. 956-968, 2014.   DOI
2 W.-J. Chang, C.-P. Kuo, and C.-C. Ku, "Intelligent fuzzy control with imperfect premise matching concept for complex nonlinear multiplicative noised systems," Neurocomputing, vol. 154, pp. 276-283, 2015.   DOI
3 D. Zhang and Q.-L. Han, "$H{\infty}$ control design for network-based T-S fuzzy systems with asynchronous constraints on membership functions," IECON 2011-37th Annual Conference on IEEE Industrial Electronics Society, pp. 2584-2589, 2011.
4 H. K. Lam and W. K. Ling, "Sampled-data fuzzy controller for continuous nonlinear systems," IET Contrl Theory Appl., vol. 2, no. 1, pp. 32-39, 2008.   DOI
5 H. Liu, F. Sun, and Z. Sun, "Stability analysis and synthesis of fuzzy singularly perturbed systems," IEEE Trans. Fuzzy Syst., vol. 13, no. 2, pp. 273-284, Apr 2005.   DOI
6 W. D. McComb, "The physics of fluid turbulence," Chem. Phys., vol. 1, 1990.
7 W. Assawinchaichote and S. K. Nguang, "$H_{\infty}$ fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: an LMI approach," IEEE Trans. Syst., Man, Cybern. B, vol. 34, pp. 579-588, 2004.   DOI
8 W. Assawinchaichote, S. K. Nguang, and P. Shi, "$H_{\infty}$ output feedback control design for uncertain fuzzy singularly perturbed systems: an LMI approach," Automatica, vol. 40, pp. 2147-2152, 2004.
9 M. Suzuki and M. Miura, "Stabilizing feedback controllers for singularly perturbed linear constant systems,"IEEE Trans. Autom. Control, vol. 21, pp. 123-124, 1976.   DOI
10 J. O'Reilly, "Full-order observers for a class of singularly perturbed linear time-varying systems," Int. J. Control, vol. 30, pp. 745-756, 1979.   DOI
11 Z. H. Shao and M. E. Sawan, "Robust stability of singularly perturbed systems," Int. J. Control, vol. 58, pp. 1469-1476, 1993.   DOI
12 M. H. Asemani and V. J. Majd, "A robust $H_{\infty}$ non-pdc design scheme for singularly perturbed T-S fuzzy systems with immeasurable state variables," IEEE Trans. Fuzzy Syst., vol. 23, pp. 525-541, 2015.   DOI
13 T. Grodt and Z. Gajic, "The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation," IEEE Trans. Autom. Control, vol. 33, pp. 751-754, 1988.   DOI
14 W. Assawinchaichote and S. K. Nguang, "Fuzzy observerbased controller design for singularly perturbed nonlinear systems: An LMI approach," Proc. of the 41th IEEE Conf. on Decision and Control, vol. 2, pp. 2165-2170, 2002.
15 T. H. S. Li and K. J. Lin, "Composite fuzzy control of nonlinear singularly perturbed systems," IEEE Trans. Fuzzy Syst., vol. 15, pp. 176-187, 2007.   DOI
16 E. Fridman, "Near-optimal $H_{\infty}$ control of linear singularly perturbed systems," IEEE Trans. Autom. Control, vol. 41, no. 2, pp. 236-240, 1996.   DOI
17 W. Tan, T. Leung, and Q. Tu, "$H_{\infty}$ control for singularly perturbed systems," Automatica, vol. 34, no. 2, pp. 255-260, 1998.   DOI
18 H. Liu, F. Sun, and Y. Hu, "$H_{\infty}$ control for fuzzy singularly perturbed systems," Fuzzy Sets Syst., vol. 155, no. 2, pp. 272-291, 2005.   DOI
19 D. W. Kim and H. J. Lee, "Direct discrete-time design approach to robust $H_{\infty}$ sampled-data observer-based output-feedback fuzzy control," Int. J. Syst. Sci., vol. 47, pp. 1-15, 2015.
20 H. J. Lee and D. W. Kim, "Performance -recoverable intelligent digital redesign for fuzzy tracking controllers," Inform. Sci., vol. 326, pp. 350-367, 2016.   DOI
21 E. Fridman, "Robust $H{\infty}$ sampled-data control of linear singularly perturbed systems," IEEE Trans. Autom. Control, vol. 51, no. 3, pp. 470-475, 2006.   DOI
22 S. C. Jee and H. J. Lee, "Sampled-data H_/$H_{\infty}$ Hfault detection and isolation for nonlinear systems in T-S form: An approximate model approach," Fuzzy Sets Syst., 2016.
23 S. C. Jee, H. J. Lee, and D. W. Kim, "Detecting sensor fault for nonlinear systems in T-S form under sampled-data measurement: exact direct discrete-time design approach," Int. J. Control Autom. Syst., vol. 14, no. 2, pp. 1-9, 2016.   DOI
24 E. Fridman, "Robust sampled-data control of linear singularly perturbed systems," in Proceedings of the 44th IEEE conference on decision and control, 2005, pp. 4324-4329.
25 J. H. Moon, J. J. Lee and H. J. Lee, "Sampled-Data Controller Design for Nonlinear Systems Including Singular Perturbation in Takagi-Sugeno Form," Journal of Korean Institute of Intelligent Systems, vol. 26, pp. 050-055, 2016.   DOI
26 K. Gu, "An integral inequality in the stability problem of time-delay systems," in Proc. of the 39th IEEE Conf. on Decision and Control, 2000, pp. 2805-2810.
27 B.-S. Chen, C.-S. Tseng, and H.-J. Uang, "Robustness design of nonlinear dynamic systems via fuzzy linear control," IEEE Trans. FuzzySyst., vol. 7, no.5, pp. 571-585, 1999.
28 K. Tanaka, T. Ikeda, and H. O. Wang, "Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs," IEEE Trans. Fuzzy Syst., vol. 6, pp. 250-265, 1998   DOI
29 D. W. Kim and H. J. Lee, "Comments on "T-S fuzzy model-based robust $H_{\infty}$ design for networked control systems with uncertainties," IEEE Trans. Ind. Informat., vol. 5, no. 4, p. 507, 2009.   DOI