Kybernetika 50 no. 4, 580-595, 2014

Non-fragile sampled data H filtering of general continuous Markov jump linear

Mouquan Shen, Guangming Zhang, Yuhao Yuan and Lei MeiDOI: 10.14736/kyb-2014-4-0580


This paper is concerned with the non-fragile sampled data $H_\infty$ filtering problem for continuous Markov jump linear system with partly known transition probabilities (TPs). The filter gain is assumed to have additive variations and TPs are assumed to be known, uncertain with known bounds and completely unknown. The aim is to design a non-fragile $H_\infty$ filter to ensure both the robust stochastic stability and a prescribed level of $H_\infty$ performance for the filtering error dynamics. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities (LMIs). An example is provided to demonstrate the effectiveness of the proposed approach.


Markov jump linear system, sampled data $H_\infty $ filtering, linear matrix equality


93E12, 62A10


  1. Y. Cao and M. Frank: Robust $H_\infty$ disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Systems 8 (2000), 406-415.   CrossRef
  2. X. Chang and G. Yang: Nonfragile $H_\infty$ filtering of continuous-time fuzzy systems. IEEE Trans. Signal Process. 59 (2011), 1528-1538.   CrossRef
  3. T. Chen and B. Francis: Optimal Sampled-Data Control Systems. Springer, London 1995.   CrossRef
  4. H. Gao, W. Sun and P. Shi: Robust sampled-data control for vehicle active suspension systems. IEEE Trans. Control Systems Technol. 18 (2010), 238-245.   CrossRef
  5. L. Hu, P. Shi and B. Huang: Stochastic stability and robust control for sampled-data systems with Markovian jump parameters. J. Math. Anal. Appl. 313 (2006), 504-517.   CrossRef
  6. Y. Ji and H. J. Chizeck: Jump linear quadratic Gaussian control: Steady-state solution and testable conditions. Control Theory Advanced Technol. 6 (1990), 289-319.   CrossRef
  7. L. H. Keel and S. P. Bhattacharyya: Robust, fragile, or optimal? IEEE Trans. Automat. Control 42 (1997), 1098-1105.   CrossRef
  8. J. Lam, Z. Shu, S. Xu and E. K. Boukas: Robust control of descriptor discrete-time Markovian jump systems. Int. J. Control 80 (2007), 374-385.   CrossRef
  9. X. Mao: Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79 (1999), 45-67.   CrossRef
  10. M. Shen and G. Yang: $H_2$ filter design for discrete Markov jump linear system with partly unknown transition probabilities. Optimal Control Appl. Methods 33 (2012), 318-337.   CrossRef
  11. B. Song, S. Xu and Y. Zou: Non-fragile $H_\infty$ filtering for uncertain stochastic time-delay systems. Int. J. Innovative Comput. Inform. and Control 5 (2009), 2257-2266.   CrossRef
  12. W. Sun, K. M. Nagpal and P. P. Khargonekar: $H_\infty$ control and filtering for sampled-data systems. IEEE Trans. Automat. Control 38 (1993), 1162-1175.   CrossRef
  13. V. Suplin, E. Fridman and U. Shaked: Sampled-data $H_\infty$ control and filtering: Nonuniform uncertain sampling. Automatica 43 (2007), 1072-1083   CrossRef
  14. J. Xiong, J. Lam, H. Gao and D. W. C. Ho: On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41 (2005), 897-903.   CrossRef
  15. S. Xu and T. Chen: Robust $H_\infty$ filtering for uncertain impulsive stochastic systems under sampled measurements. Automatica 39 (2003), 509-516   CrossRef
  16. S. Xu and T. Chen: Robust control for uncertain discrete-time stochastic bilinear systems with Markovian switching. Int. J. Robust Nonlinear 15 (2005), 201-217.   CrossRef
  17. G. Yang and W. Che: Non-fragile $H_\infty$ filter design for linear continuous-time systems. Automatica 44 (2008), 2849-2856.   CrossRef
  18. P. Shi: Filtering on sampled-data systems with parametric uncertainty. IEEE Trans. Automat. Control 43 (1998), 1022-1027.   CrossRef
  19. P. Shi, E. K. Boukas and R. K. Agarwal: Kalman filtering for continuous-time uncertain systems with Markovian jumping parameters. IEEE Trans. Automat. Control 44 (1999), 1592-1597.   CrossRef