ROBUST DELAY-DEPENDENT H∞ CONTROL DESIGN FOR UNCERTAIN TAKAGI-SUGENO TIME-DELAY SYSTEMS

Takagi-Sugeno (T-S) fuzzy modeling is a useful tool to represent complex nonlinear systems into a class of linear subsystems with fuzzy sets and reasoning. Presented is an extension of the T-S fuzzy modeling approach for uncertain nonlinear systems with state time-varying delay to derive robust delay-dependent H_∞ control methodology. To this end, we investigate the stability and performance conditions for uncertain T-S fuzzy systems with time-varying delay by the Lyapunov-Krasovskii functional. Then, the stabilization is fulfilled through a fuzzy state-feedback controller. For the synthesis condition, one of the recently developed methods is utilized, and that the solution is dependent on the size and change rate of the delay. The formulations are performed based on the solution of linear matrix inequalities (LMIs). Finally, two numerical examples are presented to validate the effectiveness of the proposed design.

Keywords:

Robust control, time-delay systems Takagi-Sugeno fuzzy systems,

PDF

___

[1] Richard, J. P., (2003) Time-delay systems: an overview of some recent advances and open problems, Automatica 39(10), 1667-1694.
[2] Cao, Y. Y., Frank, P. M., (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models, Fuzzy Sets and Systems 124(2), 213-229.
[3] Guan, X. P., Chen, C. L., (2004) Delay-dependent guaranteed cost control for TS fuzzy systems with time delays, IEEE Transactions on Fuzzy Systems 12(2), 236-249.
[4] Li, X., Gao, H., Gu, K., (2016) Delay-independent stability analysis of linear time-delay systems based on frequency discretization, Automatica 70, 288-294.
[5] Gouaisbaut, F., Peaucelle, D., (2006) Delay-dependent stability analysis of linear time delay systems, IFAC Proceedings Volumes 39(10), 54-59.
[6] Kwon, O. M., Park, M. J., Park, J. H., Lee, S. M., (2016) Stability and stabilization of TS fuzzy systems with time-varying delays via augmented Lyapunov-Krasovskii functionals, Information Sciences 372, 1-15.
[7] Yang, J., Luo, W. P., Shi, K. B., Zhao, X., (2016) Robust stability analysis of uncertain TS fuzzy systems with time-varying delay by improved delay-partitioning approach. Journal of Nonlinear Sciences & Applications (JNSA) 9(1), 171-185.
[8] Lian, Z., He, Y., Zhang, C. K., Wu, M., (2017) Further robust stability analysis for uncertain Takagi–Sugeno fuzzy systems with time-varying delay via relaxed integral inequality, Information Sciences 409, 139-150.
[9] Zhang, C. K., He, Y., Jiang, L., Wang, Q. G., Wu, M., (2017) Stability analysis of discrete-time neural networks with time-varying delay via an extended reciprocally convex matrix inequality, IEEE Transactions on Cybernetics 47(10), 3040-3049.
[10] Gu, K., Chen, J., Kharitonov, V. L., (2003) Stability of time-delay systems. Springer Science & Business Media.
[11] Seuret, A., Gouaisbaut, F., (2013) Wirtinger-based integral inequality: Application to time-delay systems, Automatica 49(9), 2860-2866.
[12] Liu, K., Seuret, A., Xia, Y., (2017) Stability analysis of systems with time-varying delays via the second-order Bessel–Legendre inequality, Automatica 76, 138-142.
[13] Park, P., Lee, W. I., Lee, S. Y., (2015) Auxiliary function-based integral inequalities for quadratic functions and their applications to time-delay systems, Journal of the Franklin Institute 352(4), 1378-1396.
[14] Wang, H. O., Tanaka, K., Griffin, M. F., (1996) An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems 4(1), 14-23.
[15] Tanaka, K., Sugeno, M. (1992) Stability analysis and design of fuzzy control systems, Fuzzy Sets and Systems 45(2), 135-156.
[16] Tanaka, K., Wang, H. O., (2004) Fuzzy control systems design and analysis: a linear matrix inequality approach, John Wiley & Sons, New York, NY, USA
[17] Guan, X. P., Chen, C. L., (2004) Delay-dependent guaranteed cost control for TS fuzzy systems with time delays, IEEE Transactions on Fuzzy Systems 12(2), 236-249.
[18] Hong, S. K., Langari, R., (2000) An LMI-based H∞ fuzzy control system design with TS framework, Information Sciences 123(3-4), 163-179.
[19] Kau, S. W., Lee, H. J., Yang, C. M., Lee, C. H., Hong, L., Fang, C. H., (2007) Robust H∞ fuzzy static output feedback control of TS fuzzy systems with parametric uncertainties, Fuzzy Sets and Systems 158(2), 135-146.
[20] Saifia, D., Chadli, M., Karimi, H. R., Labiod, S., (2015) Fuzzy control for electric power steering system with assist motor current input constraints, Journal of the Franklin Institute 352(2), 562-576.
[21] Precup, R. E., Sabau, M. C., Petriu, E. M., (2015) Nature-inspired optimal tuning of input membership functions of Takagi-Sugeno-Kang fuzzy models for anti-lock braking systems, Applied Soft Computing 27, 575-589.
[22] Wang, W. Y., Chen, M. C., Su, S. F., (2012) Hierarchical T–S fuzzy-neural control of anti-lock braking system and active suspension in a vehicle, Automatica 48(8), 1698-1706.
[23] Coskun, S., Langari, R., (2018) Improved vehicle lateral dynamics with Takagi-Sugeno $\mathscr {H} _ {\infty}$ fuzzy control strategy for emergency maneuvering. In 2018 IEEE Conference on Control Technology and Applications (CCTA) (pp. 859-864). IEEE, 21-24 August 2018, Copenhagen, Denmark.
[24] Mirzaee, A., Dehghani, M., Mohammadi, M., (2020) Robust LPV control design for blood glucose regulation considering daily life factors, Biomedical Signal Processing and Control 57, 101830.
[25] Tasoujian, S., Salavati, S., Franchek, M. A., & Grigoriadis, K. M., (2020) Robust delay-dependent LPV synthesis for blood pressure control with real-time Bayesian parameter estimation, IET Control Theory & Applications 14(10), 1334-1345.
[26] Liu, X., (2008) Delay-dependent H∞ control for uncertain fuzzy systems with time-varying delays, Nonlinear Analysis: Theory, Methods & Applications 68(5), 1352-1361.
[27] Zhang, D. W., Hao, X. H., Jia, X. C., (2008) Delay-dependent robust H∞ control for uncertain TS fuzzy systems with time-varying delay, In 2008 7th World Congress on Intelligent Control and Automation (pp. 4347-4351), IEEE, 25-27 June 2008, Chongqing, China.
[28] Chen, B., Liu, X., (2005) Delay-dependent robust H/sub/spl infin//control for TS fuzzy systems with time delay. IEEE Transactions on Fuzzy Systems 13(4), 544-556.
[29] Peng, C., Yue, D., Tian, Y. C., (2008) New approach on robust delay-dependent ${H} _\infty $ control for uncertain T-S fuzzy systems with interval time-varying delay, IEEE Transactions on Fuzzy Systems 17(4), 890-900.
[30] Li, L., Liu, X., Chai, T., (2009) New approaches on H∞ control of T–S fuzzy systems with interval time-varying delay, Fuzzy Sets and Systems 160(12), 1669-1688.
[31] Lee, W. I., Lee, S. Y., Park, P., (2014) Improved criteria on robust stability and H∞ performance for linear systems with interval time-varying delays via new triple integral functionals, Applied Mathematics and Computation 243, 570-577.
[32] Zope, R., Mohammadpour, J., Grigoriadis, K., Franchek, M., (2012) Delay-dependent H∞ control for LPV systems with fast-varying time delays, In 2012 American Control Conference (ACC) (pp. 775-780), IEEE, 27-29 June 2012, Montreal, QC, Canada
[33] Grant, M., Boyd, S., (2014) CVX: Matlab software for disciplined convex programming, version 2.1.
[34] Ramezanifar, A., Mohammadpour, J., Grigoriadis, K. M., (2013) Sampled-data control of linear parameter varying time-delay systems using state feedback, In 2013 American Control Conference (ACC) (pp. 6847-6852), IEEE, 17-19 June 2013, Washington, DC, USA.
[35] Tuan, H. D., Apkarian, P., Nguyen, T. Q., (2001) Robust and reduced-order filtering: new LMI-based characterizations and methods, IEEE Transactions on Signal Processing 49(12), 2975-2984.
[36] Xie, L., (1996) Output feedback H∞ control of systems with parameter uncertainty, International Journal of Control 63(4), 741-750.