On asynchronous l 2 − l ∞ filtering for networked fuzzy systems with Markov jump parameters over a finite-time interval

Jing Wang; Feng Li; Yonghui Sun; Hao Shen

On asynchronous $l 2 − l ∞$ filtering for networked fuzzy systems with Markov jump parameters over a finite-time interval

View Fulltext

Author(s): Jing Wang ^{1, 2} ; Feng Li ¹ ; Yonghui Sun ² ; Hao Shen ¹
- Affiliations: 1: School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan 243002, People's Republic of China ;
  2: College of Energy and Electrical Engineering, Hohai University, Nanjing 210098, People's Republic of China
Source: Volume 10, Issue 17, 21 November 2016, p. 2175 – 2185
DOI: 10.1049/iet-cta.2016.0016 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 05/01/2016, Accepted 03/06/2016, Revised 07/05/2016, Published 15/06/2016

In this study, the problem of asynchronous $l 2 − l ∞$ filtering is investigated for discrete-time networked Takagi–Sugeno fuzzy Markov jump systems (FMJSs). The system measurements are transmitted over an unreliable communication network affected by sensor non-linearity and packet dropouts. The purpose is to design an asynchronous $l 2 − l ∞$ filter for discrete-time FMJSs such that the resulting filtering error system is not only finite-time bounded for the given conditions, but also satisfies a prescribed $l 2 − l ∞$ performance. Some sufficient conditions for the existence of the asynchronous $l 2 − l ∞$ filter are presented, and the corresponding design problem is converted into a convex optimisation one. Finally, a numerical example and a modified inverted pendulum model are utilised to demonstrate the usefulness of our proposed approach.

References

1. 1)
  - 41. Yang, G.-H., Che, W.W.: ‘Non-fragile H∞ filter design for linear continuous-time systems’, Automatica, 2008, 44, pp. 2849–2856.
2. 2)
  - 25. Arrifano, N.S., Oliveira, V.A.: ‘Robust fuzzy control approach for a class of Markovian jump nonlinear systems’, IEEE Trans. Fuzzy Syst., 2006, 14, (6), pp. 738–754.
3. 3)
  - 34. He, S., Xu, H.: ‘Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach’, Nonlinear Dyn., 2015, 80, (3), pp. 1159–1171.
4. 4)
  - 20. Zhao, X., Zhang, L., Shi, P., et al: ‘Novel stability criteria for T–S fuzzy systems’, IEEE Trans. Fuzzy Syst., 2014, 22, (2), pp. 313–323.
5. 5)
  - 16. Lam, H.-K., Leung, F.H.F.: ‘Design and stabilization of sampled-data neural-network-based control systems’, IEEE Trans. Syst. Man Cybern. B, Cybem., 2006, 36, pp. 995–1005.
6. 6)
  - 21. Nguang, S.K., Assawinchaichote, W., Shi, P., et al: ‘Robust H∞ control design for uncertain fuzzy systems with Markovian jumps: an LMI approach’. Proc. of the American Control Conf., 2005, pp. 1805–1810.
7. 7)
  - 45. Liu, J., Laghrouche, S., Wack, M.: ‘Observer-based higher order sliding mode control of power factor in three-phase AC/DC converter for hybrid electric vehicle applications’, Int. J. Control, 2014, 87, (6), pp. 1117–1130.
8. 8)
  - 30. Wu, Z.-G., Shi, P., Su, H., et al: ‘Asynchronous l2−l∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities’, Automatica, 2014, 50, (1), pp. 180–186.
9. 9)
  - 38. Lubomír, B., De la Sen, M.: ‘Decentralized resilient H-infinity observer-based control for a class of uncertain interconnected networked systems’. Proc. of the 2010 American Control Conf., 2010, pp. 1338–1343.
10. 10)
  - 19. Yang, X., Wu, L., Lam, H.-K., et al: ‘Stability and stabilization of discrete-time T–S fuzzy systems with stochastic perturbation and time-varying delay’, IEEE Trans. Fuzzy Syst., 2014, 22, (1), pp. 124–138.
11. 11)
  - 15. Zhong, X., He, H., Zhang, H., et al: ‘Optimal control for unknown discrete-time nonlinear Markov jump systems using adaptive dynamic programming’, IEEE Trans. Neural Netw. Learn. Syst., 2014, 25, (12), pp. 2141–2155.
12. 12)
  - 23. Lu, R., Wu, H., Bai, J.: ‘Networked H∞ filtering for T–S fuzzy systems with quantization and data dropouts’, J. Franklin Inst., 2014, 351, (6), pp. 3126–3144.
13. 13)
  - 24. Zhang, D., Cai, W., Xie, L., et al: ‘Non-fragile distributed filtering for T–S fuzzy systems in sensor networks’, IEEE Trans. Fuzzy Syst., 2014, 23, (5), pp. 1883–1890.
14. 14)
  - 47. Qiu, J., Feng, G., Yang, J.: ‘A new design of delay-dependent robust H∞ filtering for discrete-time T–S fuzzy systems with time-varying delay’, IEEE Trans. Fuzzy Syst., 2009, 17, (5), pp. 1044–1058.
15. 15)
  - 14. You, J., Yin, S., Yu, Z.: ‘Robust estimation for discrete time-delay Markov jump systems with sensor non-linearity and missing measurements’, IET Control Theory Appl., 2014, 8, (5), pp. 330–337.
16. 16)
  - 32. Liu, X., Ho, D.W., Yu, W., et al: ‘A new switching design to finite-time stabilization of nonlinear systems with applications to neural networks’, Neural Netw., 2014, 57, pp. 94–102.
17. 17)
  - 35. Alonso-Quesada, S., Sen, De la, Ibeas, M., A.: ‘A data dropout compensation algorithm based on the iterative learning control methodology for discrete-time systems’, Math. Probl. Eng., 2015, 2015, Article ID 429892, pp. 16.
18. 18)
  - 27. Zhang, Y., Xu, S., Zhang, B.: ‘Robust output feedback stabilization for uncertain discrete-time fuzzy Markovian jump systems with time-varying delays’, IEEE Trans. Fuzzy Syst., 2009, 17, (2), pp. 411–420.
19. 19)
  - 13. Sheng, L., Zhang, W., Gao, M.: ‘Relationship between nash equilibrium strategies and control of stochastic Markov jump systems with multiplicative noise’, IEEE Trans. Autom. Control, 2014, 59, (9), pp. 2592–2597.
20. 20)
  - 48. Tanaka, K., Wang, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (John Wiely & Sons, New York, 2001).
21. 21)
  - 43. Amato, F., Ariola, M.: ‘Finite-time control of discrete-time linear systems’, IEEE Trans. Autom. Control, 2005, 50, (5), pp. 724–729.
22. 22)
  - 4. Svensson, L.E., Williams, N.: ‘Optimal monetary policy under uncertainty: a Markov jump-linear-quadratic approach’, Fed. Reserve Bank St. Louis Rev., 2008, 90, (4), pp. 275–293.
23. 23)
  - 33. Sun, Y., Li, G.: ‘Finite-time stability and stabilization of networked control systems with bounded Markovian packet dropout’, Discrete Dyn. Nat. Soc., 2014, 2014, Article ID 176919, pp. 6.
24. 24)
  - 8. Chadli, M., Guerra, T.-M.: ‘LMI solution for robust static output feedback control of Takagi–Sugeno fuzzy models’, IEEE Trans. Fuzzy Syst., 2012, 20, (6), pp. 1160–1165.
25. 25)
  - 10. Luan, X., Zhao, S., Shi, P., et al: ‘H∞ filtering for discrete-time Markov jump systems with unknown transition probabilities’, Int. J. Adapt. Control Signal Process., 2014, 28, (2), pp. 138–148.
26. 26)
  - 46. Zhang, C., Jiang, L., Wu, Q., et al: ‘Delay-dependent robust load frequency control for time delay power systems’, IEEE Trans. Power Syst., 2013, 28, (3), pp. 2192–2201.
27. 27)
  - 7. Xiong, J., Lam, J.: ‘Fixed-order robust H∞ filter design for Markovian jump systems with uncertain switching probabilities’, IEEE Trans. Signal Process., 2006, 54, (4), pp. 1421–1430.
28. 28)
  - 36. Hsu, W.-C., Lee, L.-W., Tseng, K.-H., et al: ‘Design of feedback control for networked finite-distributed delays systems with quantization and packet dropout compensation’, Discrete Dyn. Nat. Soc., 2015, 2015, Article ID 158972, pp. 15.
29. 29)
  - 44. Liu, J., Laghrouche, S., Harmouche, M., et al: ‘Adaptive-gain second-order sliding mode observer design for switching power converters’, Control Eng. Pract., 2014, 30, pp. 124–131.
30. 30)
  - 26. Shen, M., Ye, D.: ‘Improved fuzzy control design for nonlinear Markovian-jump systems with incomplete transition descriptions’, Fuzzy Sets Syst., 2013, 217, pp. 80–95.
31. 31)
  - 22. Ding, W., Mao, Z., Jiang, B., et al: ‘H∞ fault detection for a class of T–S fuzzy model-based nonlinear networked control systems’. World Congress, 2014, vol. 19, pp. 11647–11652.
32. 32)
  - 1. Gray, W.S., González, O.R., Doğan, M.: ‘Stability analysis of digital linear flight controllers subject to electromagnetic disturbances’, IEEE Trans. Aerosp. Electron. Syst., 2000, 36, (4), pp. 1204–1218.
33. 33)
  - 37. Liu, C., Xu, J., Wu, J.: ‘Iterative learning control for remote control systems with communication delay and data dropout’, Math. Probl. Eng., 2012, 2012, Article ID 705474, pp. 14.
34. 34)
  - 39. Niu, Y., Ho, D.W.: ‘Control strategy with adaptive quantizer's parameters under digital communication channels’, Automatica, 2014, 50, (10), pp. 2665–2671.
35. 35)
  - 6. Wu, L., Shi, P., Gao, H.: ‘State estimation and sliding-mode control of Markovian jump singular systems’, IEEE Trans. Autom. Control, 2010, 55, pp. 1213–1219.
36. 36)
  - 42. Tuan, H.D., Apkarian, P., Narikiyo, T., et al: ‘Parameterized linear matrix inequality techniques in fuzzy control system design’, IEEE Trans. Fuzzy Syst., 2001, 9, (2), pp. 324–332.
37. 37)
  - 11. Park, B.Y., Kwon, N.K., Park, P.: ‘Stabilization of Markovian jump systems with incomplete knowledge of transition probabilities and input quantization’, J. Franklin Inst., 2015, 352, (10), pp. 4354–4365.
38. 38)
  - 12. Shen, H., Xu, S., Lu, J., et al: ‘Passivity based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays’, J. Franklin Inst., 2012, 349, pp. 1665–1680.
39. 39)
  - 5. Ugrinovskii, V., Pota, H.R.: ‘Decentralized control of power systems via robust control of uncertain Markov jump parameter systems’, Int. J. Control, 2005, 78, (9), pp. 662–677.
40. 40)
  - 28. Yin, Y., Shi, P., Liu, F., et al: ‘Fuzzy model-based robust H∞ filtering for a class of nonlinear nonhomogeneous Markov jump systems’, Signal Process., 2013, 93, (9), pp. 2381–2391.
41. 41)
  - 18. Xie, X., Yue, D., Zhang, H., et al: ‘Control synthesis of discrete-time T–S fuzzy systems via a multi-instant homogenous polynomial approach’, IEEE Trans. Cybernet., 2016, 46, (3), pp. 630–640.
42. 42)
  - 9. Li, H., Shi, P., Yao, D., et al: ‘Observer-based adaptive sliding mode control of nonlinear Markovian jump systems’, Automatica, 2016, 64, pp. 133–142.
43. 43)
  - 31. Zhang, L., Zhu, Y., Shi, P., et al: ‘Resilient asynchronous H∞ filtering for Markov jump neural networks with unideal measurements and multiplicative noises’, IEEE Trans. Cybern., 2015, 45, (12), pp. 2840–2852.
44. 44)
  - 17. Su, X., Wu, L., Shi, P., et al: ‘Model approximation for fuzzy switched systems with stochastic perturbation’, IEEE Trans. Fuzzy Syst., 2015, 23, (5), pp. 1458–1473.
45. 45)
  - 3. Shi, Y., Yu, B.: ‘Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links’, Automatica, 2011, 47, pp. 754–760.
46. 46)
  - 29. Shu, Z., Xiong, J., Lam, J.: ‘Asynchronous output-feedback stabilization of discrete-time Markovian jump linear systems’, IEEE Conf. Decis. Control, 2012, 47, pp. 1307–1312.
47. 47)
  - 2. Shen, H., Zhu, Y., Zhang, L., et al: ‘Extended dissipative state estimation for Markov jump neural networks with unreliable links’, IEEE Trans. Neural Netw. Learn. Syst., 2016, DOI:10.1109/TNNLS.2015.2511196.
48. 48)
  - 40. Wang, Z., Dong, H., Shen, B., et al: ‘Finite-horizon H∞ filtering with missing measurements and quantization effects’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 1707–1718.

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

On asynchronous $l 2 − l ∞$ filtering for networked fuzzy systems with Markov jump parameters over a finite-time interval

References

Related content