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Novel Approach of Robust Hinf Tracking Control for Uncertain Fuzzy Descriptor Systems Using Parametric Lyapunov Function

Ho Pham Huy Anh, Cao Van Kien

Abstract


This paper proposes a novel uncertain fuzzy descriptor system which is an extension from standard T-S fuzzy system. A fixed Lyapunov function-based approach is considered and controller design for this rich class of fuzzy descriptor systems is formulated as a problem of solving a set of LMIs. The design conditions for the descriptor fuzzy system are more complicated than the standard state-space-based systems. However, the descriptor fuzzy system-based approach has the advantage of possessing fewer number of matrix inequality conditions for certain special cases. Hence, it is suitable for complex systems represented in descriptor form which is often observed in nonlinear mechanical systems.


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References


Hua, C., Zhang, L., & Guan, X. (2018). Robust Adaptive Control for Time-Delay System via TS Fuzzy Approach. In Robust Control for Nonlinear Time-Delay Systems (pp. 93-112). Springer, Singapore.

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, no. 2, pp. 250-265, May 1998.

S. Tong, T. Wang, and H. X. Li, “Fuzzy robust tracking control for uncertain nonlinear systems," Int. J. Approx. Reason., vol. 30, no. 2, pp. 73-90, Jun. 2002.

B. Zhang, S. Zhou, and T. Li, “A new approach to robust and non-fragile H∞ control for uncertain fuzzy systems," Information Sciences, vol. 177, no. 15, pp. 5118-5133, Nov. 2007.

F. Cuesta, F. Gordillo, J. Aracil, and A. Ollero, “Stability analysis of nonlinear multivariable Takagi-Sugeno fuzzy control systems," IEEE Trans. Fuzzy Syst., vol. 7, no. 5, pp. 508-520, Oct. 1999.

T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, and Cybern., vol. 15, no. 1, pp. 116-132, 1985.

J.-C. Lo and M.-L. Lin, “Robust H∞ control for fuzzy systems with Frobenius norm-bounded uncertainties," IEEE Trans. Fuzzy Syst., vol. 14, no. 1, pp. 1-15, Feb. 2006.

Zhang, X. M., Han, Q. L., & Ge, X. (2018). A Novel Finite-Sum Inequality-Based Method for Robust H∞ Control of Uncertain Discrete-Time Takagi–Sugeno Fuzzy Systems with Interval-Like Time-Varying Delays. IEEE Transactions on Cybernetics, 48(9), 2569-2582.

L. Xiaodong and Z. Qingling, ‘New approaches to H∞ controller designs based on fuzzy observers for T-S fuzzy systems via LMI," Automatica, vol. 39, pp. 1571-1582, 2003.

S. Ghosh, S. K. Das, and G. Ray, “Stabilizing adaptive controller for uncertain dynamical systems: An LMI approach," Int. J. Control, Automation and Systems, vol. 7, pp. 311-317, 2009.

A. Sala and C. Arino, “Asymptotically necessary and sufficient conditions for stability and performance in fuzzy control: Applications of Polya's theorem," Fuzzy Sets and Syst., vol. 158, pp. 2671-2686, 2007.

K. Tanaka and H. O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley-Interscience Publication, John Wiley & Sons, Inc, New York, 2001.

T. Taniguchi, K. Tanaka, and H. O. Wang, “Fuzzy descriptor systems and nonlinear model following control," IEEE Trans. Fuzzy Syst., vol. 8, no. 4, pp. 442-452, Aug. 2000.

W.-S. Yu, “Observer-based fuzzy tracking control design for nonlinear uncertain descriptor dynamic systems," in IEEE International Conf. on Systems, Man and Cybernetics (ISIC 2007), Oct. 2007, pp. 127-132.

W. Tian, H. Zhang, and X. Yang, “Robust H control for fuzzy descriptor systems with time-varying delay and parameter uncertainties," in Third International Conference on Natural Computation (ICNC 2007), 2007.

L., Zhi, et al. "Robust control for TS fuzzy systems with state and input time-varying delays via delay-product-type functional method." IEEE Transactions on Fuzzy Systems (2019).

Xue, Y., Zheng, B. C., & Yu, X. (2018). Robust sliding mode control for TS fuzzy systems via quantized state feedback. IEEE Transactions on Fuzzy Systems, 26(4), 2261-2272.

Ge, C., Shi, Y., Park, J. H., & Hua, C. (2019). Robust H∞ stabilization for TS fuzzy systems with time-varying delays and memory sampled-data control. Applied Mathematics and Computation, 346, 500-512.

Nasiri, A., Nguang, S. K., Swain, A., & Almakhles, D. J. (2018). Reducing Conservatism in an Robust State-Feedback Control Design of T–S Fuzzy Systems: A Non-monotonic Approach. IEEE Transactions on Fuzzy Systems, 26(1), 386-390.

T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst., Man, and Cybern., vol. 15, no. 1, pp. 116-132, 1985.

C. S. Tseng, B. S. Chen, and H. J. Uang, “Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model," IEEE Trans. Fuzzy Syst., vol. 9, no. 3, pp. 381-392, 2001.

S. Tong, T. Wang, and H. X. Li, “Fuzzy robust tracking control for uncertain nonlinear systems," Int. J. Approx. Reason., vol. 30, no. 2, pp. 73-90, Jun. 2002.

P. Gahinet, P. Apkarian, and M. Chilali, “A parameter-dependent Lyapunov functions and real parametric uncertainty," IEEE Trans. Automat. Contr., vol. 41, no. 6, pp. 436-442, Mar 1996.

Y.-Y. Cao and Z. Lin, “A descriptor system approach to robust stability analysis and controller synthesis," IEEE Trans. Automat. Contr., vol. 49, no. 11, pp. 2081-2084, Nov. 2004.

P. Apkarian and H. D. Tuan, “Parameterized LMIs in control theory," in 37th IEEE Conference on Decision and Control, vol. 1, 1998, pp. 152-157.




DOI: https://doi.org/10.15625/1813-9663/36/1/13749 Display counter: Abstract : 56 views. PDF : 43 views.

Journal of Computer Science and Cybernetics ISSN: 1813-9663

Published by Vietnam Academy of Science and Technology