Research Papers

Fault-Distribution Dependent Reliable H Control for Takagi-Sugeno Fuzzy Systems

[+] Author and Article Information
R. Sakthivel

Department of Mathematics,
Sungkyunkwan University,
Suwon 440 746, South Korea
e-mail: krsakthivel@yahoo.com

P. Vadivel

Department of Mathematics,
Kongu Engineering College,
Erode 638 052, Tamil Nadu, India

K. Mathiyalagan, A. Arunkumar

Department of Mathematics,
Anna University—Regional Centre,
Coimbatore 641 047, Tamil Nadu, India

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received January 21, 2013; final manuscript received October 22, 2013; published online January 9, 2014. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 136(2), 021021 (Jan 09, 2014) (11 pages) Paper No: DS-13-1034; doi: 10.1115/1.4025987 History: Received January 21, 2013; Revised October 22, 2013

This paper is concerned with the problem of robust reliable H control for a class of uncertain Takagi-Sugeno (TS) fuzzy systems with actuator failures and time-varying delay. The main objective is to design a state feedback reliable H controller such that, for all admissible uncertainties as well as actuator failure cases, the resulting closed-loop system is robustly asymptotically stable with a prescribed H performance level. Based on the Lyapunov-Krasovskii functional (LKF) method together with linear matrix inequality (LMI) technique, a delay dependent sufficient condition is established in terms of LMIs for the existence of robust reliable H controller. When these LMIs are feasible, a robust reliable H controller can be obtained. Finally, two numerical examples with simulation result are utilized to illustrate the applicability and effectiveness of our obtained result.

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Takagi, T., and Sugeno, M., 1985, “Fuzzy Identification of Systems and Its Applications to Modeling and Control,” IEEE Trans. Syst. Man Cybern., 15, pp. 116–132. [CrossRef]
Sakthivel, R., Mathiyalagan, K., and Marshal Anthoni, S., 2012, “Robust Stability and Control for Uncertain Neutral Time Delay Systems,” Int. J. Control, 85, pp. 373–383. [CrossRef]
Tian, E., and Pang, C., 2006, “Delay-Dependent Stability Analysis and Synthesis of Uncertain TS Fuzzy Systems With Time-Varying Delay,” Fuzzy Sets Syst., 157, pp. 544–559. [CrossRef]
Zhou, S., Ren, W., and Lam, J., 2011, “Stabilization for T-S Model Based Uncertain Stochastic Systems,” Inf. Sci., 181, pp. 779–791. [CrossRef]
Zhao, Y., Gao, H., Lam, J., and Du, B., 2009, “Stability and Stabilization of Delayed TS Fuzzy Systems: A Delay Partitioning Approach,” IEEE Trans. Fuzzy Syst., 17, pp. 750–762. [CrossRef]
Chen, J., Sun, F., Yin, Y., and Hu, C., 2011, “State Feedback Robust Stabilisation for Discrete-Time Fuzzy Singularly Perturbed Systems With Parameter Uncertainty,” IEE Proc.: Control Theory Appl., 5, pp. 1195–1202. [CrossRef]
Kwon, O. M., Park, M. J., Lee, S. M., and Park, Ju. H., 2012, “Augmented Lyapunov-Krasovskii Functional Approaches to Robust Stability Criteria for Uncertain Takagi-Sugeno Fuzzy Systems With Time-Varying Delays,” Fuzzy Sets Syst., 201, pp. 1–19. [CrossRef]
Li, H., Liu, H., Gao, H., and Shi, P., 2012, “Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault,” IEEE Trans. Fuzzy Syst., 20, pp. 342–357. [CrossRef]
Gao, Z., Jiang, B., Qi, R., and Xu, Y., 2011, “Robust Reliable Control for a Near Space Vehicle With Parametric Uncertainties and Actuator Faults,” Int. J. Syst. Sci., 42, pp. 2113–2124. [CrossRef]
Gu, Z., Liu, J., Du, L., and Tian, E., 2011, “Fault-Distribution-Dependent Reliable Control for Time-Varying Delay System,” Control Theory Appl., 9, pp. 589–593. [CrossRef]
Su, X., Wu, L., Shi, P., and Song, Y.-D., 2012, “H Model Reduction of Takagi-Sugeno Fuzzy Stochastic Systems,” IEEE Trans. Syst., Man, Cybern., Part B: Cybern., 99, pp. 1–12.
Senthilkumar, T., and Balasubramaniam, P., 2011, “Delay-Dependent Robust H Control for Uncertain Stochastic T-S Fuzzy Systems With Time-Varying State and Input Delays,” Int. J. Syst. Sci., 42, pp. 877–887. [CrossRef]
Mathiyalagan, K., Sakthivel, R., and Marshal Anthoni, S., 2012, “Robust Exponential Stability and H Control for Switched Neutral-Type Neural Networks,” Int. J. Adapt. Control Signal Process., (in press).
Niamsup, P., and Phat, V. N., 2010, “H Control for Nonlinear Time-Varying Delay Systems With Convex Polytopic Uncertainties,” Nonlinear Anal. Theory, Methods Appl., 72, pp. 4254–4263. [CrossRef]
Phat, V. N., 2009, “Memoryless H Controller Design for Switched Nonlinear Systems With Mixed Time-Varying Delays,” Int. J. Control, 82, pp. 1889–1898. [CrossRef]
Zhao, Y., Wu, J., and Shi, P., 2009, “H Control of Non-Linear Dynamic Systems: A New Fuzzy Delay Partitioning Approach,” IEE Proc.: Control Theory Appl., 3, pp. 917–928. [CrossRef]
Senthilkumar, T., and Balasubramaniam, P., 2011, “Robust H Control for Nonlinear Uncertain Stochastic T-S Fuzzy Systems With Time Delays,” Appl. Math. Lett., 24, pp. 1986–1994. [CrossRef]
Gu, Z., Liu, J., Peng, C., and Tian, E., 2011, “Fault-Distribution Dependent Reliable Control for T-S Fuzzy Time-Delayed Systems,” ASME J. Dyn. Syst., Meas., Control, 133, pp. 1–4. [CrossRef]
Wu, Z.-G., Shi, P., Su, H., and Chu, J., 2012, “Reliable H Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay,” IEEE Trans. Fuzzy Syst., 20, pp. 22–31. [CrossRef]
Wang, Z., Liu, Y., and Yang, F., 2006, “On Designing Robust Controllers Under Randomly Varying Sensor Delay With Variance Constraints,” Int. J. Gen. Syst., 35, pp. 1–15. [CrossRef]
He, X., Wang, Z., and Zhou, D., 2009, “Robust H Filtering for Time-Delay Systems With Probabilistic Sensor Faults,” IEEE Signal Process. Lett., 16, pp. 442–445. [CrossRef]
Kwon, O. M., Lee, S. M., and Park, Ju. H., 2011, “Linear Matrix Inequality Approach to New Delay-Dependent Stability Criteria for Uncertain Dynamic Systems With Time-Varying Delays,” J. Optim. Theory Appl., 149, pp. 630–646. [CrossRef]
Duan, H., Su, H., and Wu, Z.-G., 2012, “H State Estimation of Static Neural Networks With Time-Varying Delay,” Neurocomputing, 97, pp. 16–21. [CrossRef]
Feng, Z., and Lam, J., 2012, “Integral Partitioning Approach to Robust Stabilization for Uncertain Distributed Time-Delay Systems,” Int. J. Robust Nonlinear Control, 22, pp. 676–689. [CrossRef]
Zames, G., 1981, “Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses,” IEEE Trans. Autom. Control, 26, pp. 301–320. [CrossRef]
Liu, Y., Wang, Z., and Liu, X., 2008, “Exponential Synchronization of Complex Networks With Markovian Jump and Mixed Delays,” Phys. Lett. A, 372, pp. 3986–3998. [CrossRef]
Sun, J., Liu, G. P., and Chen, J., 2009, “Delay-Dependent Stability and Stabilization of Neutral Time-Delay Systems,” Int. J. Robust Nonlinear Control, 19, pp. 1364–1375. [CrossRef]
Sun, J., Liu, G. P., Chen, J., and Rees, D., 2009, “Improved Stability Criteria for Neural Networks With Time-Varying Delay,” Phys. Lett. A, 373, pp. 342–348. [CrossRef]
Liu, Z., Yu, J., Xu, D., and Peng, D., 2013, “Triple-Integral Method for the Stability Analysis of Delayed Neural Networks,” Neurocomputing, 99, pp. 283–289. [CrossRef]


Grahic Jump Location
Fig. 1

State trajectories of x(t) of system in Example 4.1 for i = 1 and i = 2 when μ = 0.8

Grahic Jump Location
Fig. 2

Time-varying delay τ(t) in Example 4.1

Grahic Jump Location
Fig. 3

State trajectories of x(t) of system in Example 4.2 for i = 1 and i = 2 when μ = 1

Grahic Jump Location
Fig. 4

Time-varying delay τ(t) in Example 4.2




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