Robust H∞ control for class of discrete-time Markovian jump systems with time-varying delays based on delta operator

Circuits, Systems, and Signal Processing

Volumn 27, Issue 5, 2008, Pages 627-643

  Qiu, Jiqing ^a   Yang, Hongjiu ^a   Shi, Peng ^b   Xia, Yuanqing ^c  

^a HEBEI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b VICTORIA UNIVERSITY   (Australia)

^c BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Delta operators; Discrete time systems; H control; Linear fractional uncertainties; Linear matrix inequalities; Markovian jump parameters; Time varying delays

Indexed keywords

CONTINUOUS TIME SYSTEMS; CONTROL THEORY; DIGITAL CONTROL SYSTEMS; FEEDBACK; FEEDBACK CONTROL; FUZZY CONTROL; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; NONLINEAR CONTROL SYSTEMS; ROBUST CONTROL; STATE FEEDBACK; SWITCHING SYSTEMS; TIME VARYING CONTROL SYSTEMS; TIME VARYING SYSTEMS; UNCERTAIN SYSTEMS;

DELTA OPERATORS; DISCRETE-TIME SYSTEMS; LINEAR FRACTIONAL UNCERTAINTIES; MARKOVIAN JUMP PARAMETERS; TIME-VARYING DELAYS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 54249095963     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-008-9046-7     Document Type: Article

References (29)

1. M. Basin, E. Sanchez, R. Martinez-Zuniga, Optimal linear filtering for systems with multiple state and observation delays. Int. J. Innov. Comput. Inf. Control 3 (5), 1309-1320 (2007)
2. E.K. Boukas, N.F. Al-Muthairi, Delay-dependent stabilization of singular linear systems with delays. Int. J. Innov. Comput. Inf. Control 2 (2), 283-291 (2006)
3. B. Chen, J. Lam, S. Xu, Memory state feedback guaranteed cost control for neutral delay systems. Int. J. Innov. Comput. Inf. Control 2 (2), 293-303 (2006)
4. ∞ control. Int. J. Control 72 (4), 315-320 (1999)
5. H. Fan, Singular root distribution problem for delta-operator based real polynomials. Automatica 35 (5), 791-807 (1999)
6. H. Gao, T. Chen, New results on stability of discrete-time systems with time-varying state delay. IRE Trans. Automat. Contr. 52 (2), 328-334 (2007)
7. G.C. Goodwin, R.H. Middleton, Rapprochement between continuous and discrete model reference adaptive control. Automatica 22 (6), 199-207 (1986)
8. L. Hu, P. Shi, P.M. Frank, Robust sampled-data control for Markovian jump linear systems. Automatica 42 (11), 2025-2030 (2006)
9. X. Jiang, Q. Han, X. Yu, Stability criteria for linear discrete-time systems with interval-like time-varying delay, in American Control Conference (2005)
10. M. Karan, P. Shi, C.Y. Kaya, Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems. Automatica 42 (12), 2159-2168 (2006)
11. M.S. Mahmoud, P. Shi, Robust control for Markovian jump linear discrete-time systems with unknown nonlinearities. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49 (4), 538-542 (2002)
12. B. Michael, P. Joel, M.Z. Rodolfo, Optimal filtering for nonlinear polynomial systems over linear observations with delay. Int. J. Innov. Comput. Inf. Control 2 (4), 863-874 (2006)
13. J. Qiu, J. Zhang, in New Robust Stability Criterion for Uncertain Fuzzy Systems with Fast Time-varying Delays. Lecture Notes in Computer Sciences, vol. 223 (Springer, Berlin, 2006), pp. 41-44
14. J. Qiu, J. Zhang, P. Shi, Robust stability of uncertain linear systems with time-varying delay and nonlinear perturbations. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 220 (5), 411-416 (2006)
15. ∞ state feedback control of discrete time-delay linear systems with norm-bounded uncertainty. Int. J. Syst. Sci. 31 (4), 409-415 (2000)
16. P. Shi, E. Boukas, R.K. Agarwal, Control of Markovian jump discrete-time systems with norm bounded uncertainty and unknown delay. IEEE Trans. Automat. Contr. 44 (11), 2139-2144 (1999)
17. P. Shi, Y. Xia, G. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Automat. Contr. 51 (1), 97-103 (2006)
18. P. Shi, M. Mahmoud, S.K. Nguang, A. Ismail, Robust filtering for jumping systems with mode-dependent delays. Signal Process. 86 (1), 140-152 (2006)
19. C.B. Soh, Robust discrete time systems using delta operator. Int. J. Control 54 (2), 453-464 (1991)
20. C.B. Soh, Robust stability of discrete-time systems using delta operator. IEEE Trans. Automat. Contr. 35 (3), 377-380 (1991)
21. P. Suchomski, Numerically robust delta-domain solutions to discrete-time Lyapunov equations. Syst. Control. Lett. 47 (4), 319-326 (2002)
22. R. Wang, J. Zhao, Exponential stability analysis for discrete-time switched linear systems with time-delay. Int. J. Innov. Comput. Inf. Control 3 (6), 1557-1564 (2007)
23. ∞ control of networked control system via LMI approach. Int. J. Innov. Comput. Inf. Control 3 (2), 343-352 (2007)
24. ∞ control for jump linear systems with delays. Syst. Control. Lett. 55 (11), 939-948 (2006)
25. Y. Xia, Y. Jia, Robust sliding mode control for uncertain time-delay systems: An LMI approach. IEEE Trans. Automat. Contr. 48 (6), 1086-1092 (2003)
26. Y. Xia, Y. Jia, Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals. Syst. Control. Lett. 50 (3), 183-193 (2003)
27. Y. Xia, P. Shi, G.P. Liu, D. Rees, J. Han, Active disturbance rejection control for uncertain multivariable systems with time-delay. IET Control Theory Appl. 1 (1), 75-81 (2007)
28. ∞ control of systems with parameter uncertainty. Int. J. Control 63 (4), 741-750 (1996)
29. J. Xiong, J. Lam, Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers. Automatica 42 (5), 747-753 (2006)