Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts

Hao Shen; Zheng-Guang Wu; Ju H. Park

Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts

View Fulltext

Author(s): Hao Shen ^{1, 2} ; Zheng-Guang Wu ³ ; Ju H. Park ²
- Affiliations: 1: School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, People's Republic of China;
  2: Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 712-749, Republic of Korea;
  3: National Laboratory of Industrial Control Technology, Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou Zhejiang, 310027, People's Republic of China
Source: Volume 8, Issue 16, 06 November 2014, p. 1617 – 1624
DOI: 10.1049/iet-cta.2013.1068 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 29/11/2013, Accepted 22/05/2014, Revised 07/04/2014, Published 04/08/2014

This study is concerned with the finite-time energy-to-peak filtering problem for Markov jump repeated scalar non-linear systems with packet dropouts. The packet dropout phenomenon occurs in a random way and is modelled by a stochastic variable satisfying the Bernoulli distribution. The purpose of the study is to design a filter such that the resulting filtering error system is stochastically finite-time bounded, and a prescribed energy-to-peak performance level is achieved over a finite time interval. By using the mode-dependent diagonally dominant Lyapunov function approach, some strict linear matrix inequality-based conditions are established for the existence of an admissible filter, and a corresponding explicit parameterisation of such a filter is obtained. Finally, a numerical example with simulation is presented to demonstrate the effectiveness of our proposed approach.

References

1. 1)
  - 41. Shen, H., Xu, S., Lu, J., Zhou, J.: ‘Passivity based control for uncertain stochastic jumping systems with mode-dependent round-trip time delays’, J. Franklin Inst., 2012, 349, pp. 1665–1680 (doi: 10.1016/j.jfranklin.2011.11.011).
2. 2)
  - H. Gao , J. Lam , C. Wang . Robust energy-to-peak filter design for stochastic time-delay systems. Syst. Control Lett. , 101 - 111
3. 3)
  - H. Gao , J. Lam , C. Wang . Induced l2 and generalized ℋ2 filtering for systems with repeated scalar nonlinearities. IEEE Trans. Signal Process. , 11 , 4215 - 4226
4. 4)
  - L. Wu , P. Shi , H. Gao , C. Wang . ℋ∞ filtering for 2D Markovian jump systems. Automatica , 7 , 1849 - 1858
5. 5)
  - 37. Shen, H., Xu, S., Zhou, J., Lu, J.: ‘Fuzzy ℋ∞ filtering for nonlinear Markovian jump neutral systems’, Int. J. Syst. Sci., 2011, 42, pp. 767–780 (doi: 10.1080/00207721003790351).
6. 6)
  - L. Wu , X. Yao , W. Zheng . Generalized H2 fault detection for two-dimensional Markovian jump systems. Automatica , 8 , 1741 - 1750
7. 7)
  - 33. Dong, H., Wang, Z., Gao, H.: ‘ℋ∞ filtering for systems with repeated scalar nonlinearities under unreliable communication links’, Signal Process., 2009, 89, (8), pp. 1567–1575 (doi: 10.1016/j.sigpro.2009.02.011).
8. 8)
  - 28. Wei, Y., Wang, M., Qiu, J.: ‘New approach to delay-dependent ℋ∞ filtering for discrete-time Markovian jump systems with time-varying delay and incomplete transition descriptions’, IET Control Theory Appl., 2013, 7, (5), pp. 684–696 (doi: 10.1049/iet-cta.2012.0621).
9. 9)
  - M. Liu , D.W.C. Ho , Y. Niu . Stabilization of Markovian jump linear system over networks with random communication delay. Automatica , 2 , 416 - 421
10. 10)
  - 27. Wang, Z., Dong, H., Shen, B., Gao, H.: ‘Finite-horizon ℋ∞ filtering with missing measurements and quantization effects’, IEEE Trans. Autom. Control, 2013, 58, (7), pp. 1707–1718 (doi: 10.1109/TAC.2013.2241492).
11. 11)
  - Y. Shi , B. Yu . Output feedback stabilization of networked control systems with random delays modeled by Markov chains. IEEE Trans. Autom. Control , 1668 - 1674
12. 12)
  - 42. Li, F., Wu, L., Shi, P.: ‘Stochastic stability of semi-Markovian jump systems with mode-dependent delays’, Int. J. Robust Nonlinear Control, in press, 2013, doi: 10.1002/rnc.3057.
13. 13)
  - 39. Shen, H., Song, X., Wang, Z.: ‘Robust fault tolerant control of uncertain fractional-order systems against actuator faults’, IET Control Theory Appl., 2013, 7, (9), pp. 1233–1241 (doi: 10.1049/iet-cta.2012.0822).
14. 14)
  - 25. Zhao, S., Liu, F.: ‘State estimation in non-linear Markov jump systems with uncertain switching probabilities’, IET Control Theory Appl., 2012, 6, (5), pp. 641–650 (doi: 10.1049/iet-cta.2011.0333).
15. 15)
  - W. Li , Y. Jia . State estimation for jump Markov linear systems by variational Bayesian approximation. IET Control Theory Appl. , 319 - 326
16. 16)
  - 30. Zhang, Y., He, Y., Wu, M., Zhang, J.: ‘State estimation for Markovian jump systems with time-varying delay and partial information on transition probabilities’, IET Control Theory Appl., 2012, 6, (16), pp. 2549–2555 (doi: 10.1049/iet-cta.2011.0717).
17. 17)
  - L.X. Zhang , J. Lam . Necessary and sufficient conditions for analysis and synthesis of Markov jump linear systems with incomplete transition descriptions. IEEE Trans. Autom. Control , 7 , 1695 - 1701
18. 18)
  - 20. Xu, S., Lam, J.: ‘Robust control and filtering of singular systems’ (Berlin, Springer-Verlag, 2006).
19. 19)
  - 11. Zhang, B., Zheng, W., Xu, S.: ‘Filtering of Markovian jump delay systems based on a new performance index’, IEEE Trans. Circuits Syst. I, 2013, 54, (9), pp. 1250–1263 (doi: 10.1109/TCSI.2013.2246213).
20. 20)
  - H. Zhang , Y. Shi , A. Saadat Mehr . Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data. IET Control Theory Appl. , 12 , 2921 - 2936
21. 21)
  - R. Yang , P. Shi , G. Li . Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts. IEEE Trans. Autom. Control , 2655 - 2660
22. 22)
  - F. Amato , M. Ariola . Finite-time control of discrete-time linear systems. IEEE Trans. Autom. Control , 1 , 724 - 729
23. 23)
  - 22. Shen, B., Wang, Z., Ding, D., Shu, H.: ‘H∞ state estimation for complex networks with uncertain inner coupling and incomplete measurements’, IEEE Trans. Neural Netw. Learn. Syst., 2013, 24, (12), pp. 2027–2037 (doi: 10.1109/TNNLS.2013.2271357).
24. 24)
  - L.E. Ghaoui , F. Oustry , M. AitRami . A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
25. 25)
  - Y. Shi , B. Yu . Robust mixed H2/H∞ control of networked control systems with random time delays in both forward and backward communication links. Automatica , 4 , 754 - 760
26. 26)
  - 25. Wu, Z., Lam, J., Su, H., Chu, J.: ‘Stability and dissipativity analysis of static neural networks with time delay’, IEEE Trans. Neural Netw. Learn. Syst., 2012, 47, (2), pp. 199–210 (doi: 10.1109/TNNLS.2011.2178563).
27. 27)
  - S.P. Ma , E.K. Boukas . Robust ℋ∞ filtering for uncertain discrete Markov jump singular systems with mode-dependent time delay. IET Control Theory Appl. , 3 , 351 - 361
28. 28)
  - 21. Choi, M., Choi, J., Chung, W.: ‘State estimation with delayed measurements incorporating time-delay uncertainty’, IET Control Theory Appl., 2012, 6, (15), pp. 2351–2361 (doi: 10.1049/iet-cta.2010.0278).
29. 29)
  - Y. Xia , M. Fu , P. Shi , Z. Wu , J. Zhang . Adaptive backstepping controller design for stochastic jump systems. IEEE Trans. Autom. Control , 12 , 2853 - 2859
30. 30)
  - 2. Dong, H., Wang, Z., Gao, H.: ‘Filtering, control and fault detection with randomly occurring incomplete information’ (Wiley, Chichester, 2013).
31. 31)
  - 41. Shen, H., Park, J., Zhang, L.X., Wu, Z.: ‘Robust extended dissipative control for sampled-data Markov jump systems’, Int. J. Control, 1997, 42, (8), pp. 1171–1176.
32. 32)
  - 43. Huang, J., Shi, Y.: ‘Stochastic stability and robust stabilization of semi-Markov jump linear systems’, Int. J. Robust Nonlinear Control, 2013, 23, (18), pp. 2028–2043 (doi: 10.1002/rnc.2862).
33. 33)
  - G. Wang , Q. Zhang . Adaptive state estimation for stochastic delay systems with state-dependent Markovian switching. IET Control Theory Appl. , 6 , 822 - 828
34. 34)
  - 13. Chu, Y.C., Glover, K.: ‘Stabilization and performance synthesis for systems with repeated scalar nonlinearities’, IEEE Trans. Autom. Control, 1999, 44, (3), pp. 484–496 (doi: 10.1109/9.751343).
35. 35)
  - 30. Wu, Z., Shi, P., Su, H., Chu, J.: ‘Asynchronous l2 − l∞ filtering for discrete-time stochastic Markov jump systems with randomly occurred sensor nonlinearities’, Automatica, 2013, 50, (1), pp. 180–186 (doi: 10.1016/j.automatica.2013.09.041).
36. 36)
  - 17. Wu, L.G., Su, X.J., Shi, P.: ‘Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems’, Automatica, 2012, 48, (8), pp. 1929–1933 (doi: 10.1016/j.automatica.2012.05.064).
37. 37)
  - 22. Luan, X., Shi, P., Liu, F.: ‘Finite-time stabilisation for Markov jump systems with Gaussian transition probabilities’, IET Control Theory Appl., 2013, 7, (2), pp. 298–304 (doi: 10.1049/iet-cta.2012.0509).
38. 38)
  - L.G. Wu , P. Shi , H.J. Gao . State estimation and sliding-mode control of Markovian jump singular systems. IEEE Trans. Autom. Control , 5 , 1213 - 1219
39. 39)
  - 19. Wu, L., Su, X., Shi, P.: ‘Output feedback control of Markovian jump repeated scalar nonlinear systems’, IEEE Trans. Automat. Control, 2014, 59, (1), pp. 199–204 (doi: 10.1109/TAC.2013.2267353).
40. 40)
  - H. Dong , Z. Wang , H. Gao . H∞ fuzzy control for systems with repeated scalar nonlinearities and random packet losses. IEEE Trans. Fuzzy Syst. , 2 , 440 - 450
41. 41)
  - Y. Niu , D.W.C. Ho , X. Wang . Sliding mode control for Itô stochastic systems with Markovian switching. Automatica , 1784 - 1790
42. 42)
  - 12. Chu, Y.C., Glover, K.: ‘Bounds of the induced norm and model reduction errors for systems with repeated scalar nonlinearities’, IEEE Trans. Autom. Control, 1999, 44, (3), pp. 471–483 (doi: 10.1109/9.751342).
43. 43)
  - 5. Chu, Y.: ‘Further results for systems with repeated scalar nonlinearities’, IEEE Trans. Autom. Control, 2001, 46, (12), pp. 2031–2035 (doi: 10.1109/9.975515).

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Finite-time energy-to-peak filtering for Markov jump repeated scalar non-linear systems with packet dropouts

References

Related content