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Robust Control for Discrete-Time T-S Fuzzy Singular Systems

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Abstract

This paper deals with the robust admissibility and state feedback stabilization problems for discrete-time T-S fuzzy singular systems with norm-bounded uncertainties. By introducing a new approximation technique, the initial membership functions are conveniently expressed in piecewiselinear functions with the consideration of the approximation errors. By utilizing the piecewise-linear membership functions, the fuzzy weighting-based Lyapunov function and the use of auxiliary matrices, the admissibility of the systems is determined by examining the conditions at some sample points. The conditions can be reduced into the normal parallel distributed compensation ones by choosing special values of some slack matrices. Furthermore, the authors design the robust state feedback controller to guarantee the closed-loop system to be admissible. Two examples are provided to illustrate the advantage and effectiveness of the proposed method.

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References

  1. Takagi T and Sugeno M, Fuzzy identification of systems and its applications to modeling and control, IEEE Transactions on Systems Man and Cybernetics, 1985, 15(1): 116–132.

    Article  MATH  Google Scholar 

  2. Ma H, Li H, Liang H, et al., Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults, IEEE Transactions on Fuzzy Systems, 2019, 27(11): 2242–2254.

    Article  Google Scholar 

  3. Liang H, Zhang L, Sun Y, et al., Containment control of semi-markovian multiagent systems with switching topologies, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, https://doi.org/10.1109/TSMC.2019.2946248.

  4. Zhu W, Wang D, and Zhou Q, Leader-following consensus of multi-agent systems via adaptive event-based control, Journal of Systems Science and Complexity, 2019, 32(3): 846–856.

    Article  MathSciNet  MATH  Google Scholar 

  5. Xu X, Liu L, and Feng G, Consensus of single integrator multi-agent systems with unbounded transmission delays, Journal of Systems Science and Complexity, 2019, 32(3): 778–788.

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhang Z, Lin C, and Chen B, New decentralized H filter design for nonlinear interconnected systems based on Takagi-Sugeno fuzzy models, IEEE Transactions on Cybernetics, 2015, 45(12): 2914–2924.

    Article  Google Scholar 

  7. Dong J, Wu Y, and Yang G H, A new sensor fault isolation method for T-S fuzzy systems, IEEE Transactions on Cybernetics, 2017, 47(9): 2437–2447.

    Article  Google Scholar 

  8. Zhang L, Lam H K, Sun Y, et al., Fault detection for fuzzy semi-Markov jump systems based on interval type-2 fuzzy approach, IEEE Transactions on Fuzzy Systems, 2019, https://doi.org/10.1109/TFUZZ.2019.2936333.

  9. Yu J, Shi P, Dong W, et al., Command filtering-based fuzzy control for nonlinear systems with saturation input, IEEE Transactions on Cybernetics, 2017, 47(9): 2472–2479.

    Article  Google Scholar 

  10. Vrkalovic S, Teban T A, and Borlea L D, Stable Takagi-Sugeno fuzzy control designed by optimization, International Journal of Artificial Intelligence, 2017, 15(2): 17–29.

    Google Scholar 

  11. Zhao T and Dian S, Fuzzy static output feedback H control for nonlinear systems subject to parameter uncertainties, Journal of Systems Science and Complexity, 2018, 31(2): 343–371.

    Article  MathSciNet  MATH  Google Scholar 

  12. Taniguchi T, Tanaka K, and Wang H, Fuzzy descriptor systems and nonlinear model following control, IEEE Transactions on Fuzzy Systems, 2000, 8: 442–452.

    Article  Google Scholar 

  13. Wang H O, Tanaka K, and Griffin M F, An approach to fuzzy control of nonlinear systems: Stability and design issues, IEEE Transactions on Fuzzy Systems, 1996, 4(1): 14–23.

    Article  Google Scholar 

  14. Precup R E, Doboli S, and Preitl S, Stability analysis and development of a class of fuzzy control systems, Engineering Applications of Artificial Intelligence, 2000, 13(3): 237–247.

    Article  Google Scholar 

  15. Hao Y, Structure and stability analysis of general Mamdani fuzzy dynamic models, International Journal of Intelligent Systems, 2005, 20(1): 103–125.

    Article  MATH  Google Scholar 

  16. Zeng H B, Teo K L, He Y, et al., Sampled-data-based dissipative control of T-S fuzzy systems, Applied Mathematical Modelling, 2019, 65: 415–427.

    Article  MathSciNet  MATH  Google Scholar 

  17. Li X, Luo X, Li S, et al., Output consensus for heterogeneous nonlinear multi-agent systems based on T-S fuzzy model, Journal of Systems Science and Complexity, 2017, 30(5): 1042–1060.

    Article  MathSciNet  MATH  Google Scholar 

  18. Feng G, Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions, IEEE Transactions on Fuzzy Systems, 2014, 12(1): 22–28.

    Article  Google Scholar 

  19. Lin C, Wang Q G, Lee T H, et al., Fuzzy weighting-dependent approach to H filter design for time-delay fuzzy systems, IEEE Transactions on Signal Processing, 2007, 55: 2746–2751.

    Article  MathSciNet  MATH  Google Scholar 

  20. Rhee B J and Won S, A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design, Fuzzy Sets and Systems, 2016, 157(9): 1211–1228.

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhang Z, Lin C, and Chen B, New stability and stabilization conditions for T-S fuzzy systems with time delay, Fuzzy Sets and Systems, 2015, 263: 82–91.

    Article  MathSciNet  MATH  Google Scholar 

  22. Bernal M, Guerra T M, and Kruszewski A, A membership-function-dependent approach for stability analysis and controller synthesis of Takagi-Sugeno medels, Fuzzy Sets and Systems, 2009, 160(19): 2776–2795.

    Article  MathSciNet  MATH  Google Scholar 

  23. Lam H K and Narimani M, Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching, IEEE Transactions on Fuzzy Systems, 2009, 17: 949–961.

    Article  Google Scholar 

  24. Lam H K, Polynomial fuzzy-model-based control systems: Stability analysis via piecewise-linear membership functions, IEEE Transactions on Fuzzy Systems, 2011, 19: 588–593.

    Article  Google Scholar 

  25. Xiao B, Lam H K, and Li H, Stabilization of interval type-2 polynomial-fuzzy-model-based control systems, IEEE Transactions on Fuzzy Systems, 2017, 25: 205–217.

    Article  Google Scholar 

  26. Lam H K and Tsai S H, Stability analysis of polynomial-fuzzy model-based control systems with mismatched premise membership functions, IEEE Transactions on Fuzzy Systems, 2014, 22: 223–229.

    Article  Google Scholar 

  27. Lam H K and Li H, Output-feedback tracking control for polynomial fuzzy-model-based control systems, IEEE Transactions on Industrial Electronics, 2013, 60(12): 5830–5840.

    Article  Google Scholar 

  28. Lee D H, Joo J H, and Tak M H, Local stability analysis of continuous-time Takagi-Sugeno fuzzy systems: A fuzzy Lyapunov function approach, Information Sciences, 2014, 257: 163–175.

    Article  MathSciNet  MATH  Google Scholar 

  29. Chen J, Xu S, Zhang B, et al., Novel stability conditions for discrete-time T-S fuzzy systems: A Kronecker-product approach, Information Sciences, 2016, 337–338: 72–81.

    Article  MATH  Google Scholar 

  30. Chen J, Lin C, Chen B, et al., Regularization and stabilization for rectangular T-S fuzzy discrete-time systems with time delay, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 49(4): 833–842.

    Article  Google Scholar 

  31. Chen J, Zhang T, Zhang Z, et al., Stability and output feedback control for singular markovian jump delayed systems, Mathematical Control & Related Fields, 2018, 8: 475–490.

    Article  MathSciNet  MATH  Google Scholar 

  32. Chen J, Lin C, Chen B, et al., Mixed H and passive control for singular systems with time delay via static output feedback, Applied Mathematics & Computation, 2017, 293: 244–253.

    Article  MathSciNet  MATH  Google Scholar 

  33. Gu P, Tian S, and Liu Q, Closed-loop iterative learning control for discrete singular systems with fixed initial shift, Journal of Systems Science and Complexity, 2019, 32(2): 577–587.

    Article  MathSciNet  MATH  Google Scholar 

  34. Long S and Zhong S, H control for a class of discrete-time singular systems via dynamic feedback controller, Applied Mathematics Letters, 2016, 58: 110–118.

    Article  MathSciNet  MATH  Google Scholar 

  35. Ma Y, Jia X, and Liu D, Finite-time dissipative control for singular discrete-time Markovian jump systems with actuator saturation and partly unknown transition rates, Applied Mathematical Modelling, 2018, 53: 49–70.

    Article  MathSciNet  MATH  Google Scholar 

  36. Hsiung K L and Lee L, Lyapunov inequality and bounded real lemma for discrete-time descriptor systems, IEE Proceedings Control Theory and Applications, 1999, 146: 327–331.

    Article  Google Scholar 

  37. Feng Y and Yagoubi M, On state feedback H control for discrete-time singular systems, IEEE Transactions on Automatic Control, 2013, 58: 2674–2679.

    Article  MathSciNet  MATH  Google Scholar 

  38. Feng Z and Lam J, Dissipative control and filtering of discrete-time singular systems, International Journal of Systems Science, 2016, 47: 2532–2542.

    Article  MathSciNet  MATH  Google Scholar 

  39. Xu S, Song B, Lu J, et al., Robust stability of uncertain discrete-time singular fuzzy systems, Fuzzy Sets and Systems, 2007, 158: 2306–2316.

    Article  MathSciNet  MATH  Google Scholar 

  40. Huang C P, Stability analysis of discrete singular fuzzy systems, Fuzzy Sets and Systems, 2005, 151: 155–165.

    Article  MathSciNet  MATH  Google Scholar 

  41. Peng T, Han C, Xiong Y, et al., Filter design for discrete-time singularly perturbed T-S fuzzy systems, Journal of the Franklin Institute, 2013, 350: 3011–3028.

    Article  MathSciNet  MATH  Google Scholar 

  42. Chen J, Lin C, Chen B, et al., Fuzzy-model-based admissibility analysis and output feedback control for nonlinear discrete-time systems with time-varying delay, Information Sciences, 2017, 412–413: 116–131.

    Article  MathSciNet  MATH  Google Scholar 

  43. Zhang D, Jing Y, Zhang Q, et al., Stabilization of singular T-S fuzzy Markovian jump system with mode-dependent derivative-term coefficient via sliding mode control, Applied Mathematics and Computation, 2020, 364, Article 124643.

  44. Wang J, Ma S, and Zhang C, Finite-time H control for T-S fuzzy descriptor semi-Markov jump systems via static output feedback, Fuzzy Sets and Systems, 2019, 365: 60–80.

    Article  MathSciNet  MATH  Google Scholar 

  45. Xu S and Lam J, Robust Control and Filtering of Singular Systems, Springer, Berlin, 2006.

    MATH  Google Scholar 

  46. Lin C, Wang Q G, Lee T H, et al., LMI Approach to Analysis and Control of Takagi-Sugeno Fuzzy Systems with Time Delay, Springer-Verlag, Berlin Heidelberg, 2007.

    MATH  Google Scholar 

  47. Boyd S, Ghaoui L El, Feron E, et al., Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA: SIAM, 1994.

    Book  MATH  Google Scholar 

  48. Park G K and Sugeno M, Learning based on linguistic instructions using fuzzy theory, 8th Fuzzy System Symp., 1992, 561–564 (in Japanese).

  49. Chadli M, Karimi H R, and Shi S, On stability and stabilization of singular uncertain Takagi-Sugeno fuzzy systems, Journal of the Franklin Institute, 2014, 351: 1453–1463.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Jinpeng Yu.

Additional information

This paper was supported in part by the National Natural Science Foundation of China under Grant Nos. 61973179 and 61803220, and in part by the Taishan scholar Special Project Fund under Grant No. TSQN20161026.

This paper was recommended for publication by Editor LI Hongyi.

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Chen, J., Yu, J. Robust Control for Discrete-Time T-S Fuzzy Singular Systems. J Syst Sci Complex 34, 1345–1363 (2021). https://doi.org/10.1007/s11424-020-0059-z

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  • DOI: https://doi.org/10.1007/s11424-020-0059-z

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