Robust finite-time H∞ control for nonlinear jump systems via neural networks

Circuits, Systems, and Signal Processing

Volumn 29, Issue 3, 2010, Pages 481-498

  Luan, Xiaoli ^a   Liu, Fei ^a   Shi, Peng ^b,c  

^a JIANGNAN UNIVERSITY   (China)

^b UNIVERSITY OF GLAMORGAN   (United Kingdom)

^c VICTORIA UNIVERSITY   (Australia)

Author keywords

Finite time boundedness; Finite time stabilization; H control; Markovian jump systems; Neural networks

Indexed keywords

APPROXIMATION ERRORS; CONTROL DESIGN; CONTROLLER GAIN; EXTERNAL DISTURBANCES; FEEDBACK NEURAL NETWORK; FINITE TIME STABILIZATION; FINITE-TIME BOUNDEDNESS; JUMP SYSTEM; LINEAR DIFFERENTIAL INCLUSIONS; MARKOV JUMP SYSTEM; MARKOVIAN JUMP SYSTEMS; NON-LINEARITY; NORM BOUNDED PARAMETER UNCERTAINTY; PIECEWISE INTERPOLATION; SIMULATION RESULT; STATE-FEEDBACK CONTROLLERS;

CONTROLLERS; DISCRETE TIME CONTROL SYSTEMS; FEEDBACK; FUZZY CONTROL; LINEAR MATRIX INEQUALITIES; NONLINEAR FEEDBACK; STABILIZATION; STATE FEEDBACK;

MULTILAYER NEURAL NETWORKS;

EID: 77954563118     PISSN: 0278081X     EISSN: 15315878     Source Type: Journal    
DOI: 10.1007/s00034-010-9158-8     Document Type: Article

References (32)

1. F. Amato, M. Ariola, Finite-time control of discrete-time linear systems. IEEE Trans. Autom. Control 50 (5), 724-729 (2005)
2. F. Amato, M. Ariola, C. T. Abdallah, Dynamic output feedback finite-time control of LIT systems subject to parametric uncertainties and disturbances, in Proc. of the European Control Conference (Springer, Berlin, 1999), pp. 1176-1180
3. F. Amato, M. Ariola, P. Dorato, Finite-time control of linear systems subject to parametric uncertainties and disturbances. Automatica 37 (9), 1459-1463 (2001)
4. F. Amato, M. Ariola, C. Cosentino, Finite-time stabilization via dynamic output feedback. Automatica 42 (2), 337-342 (2006)
5. W. Assawinchaichote, S. K. Nguang, P. Shi, El K. Boukas, H-infinity fuzzy state-feedback control design for nonlinear systems with D-stability constraints: an LMI approach. Math. Comput. Simul. 78 (4), 514-531 (2008)
6. E. K. Boukas, P. Shi, K. Benjelloun, On stabilization of uncertain linear systems with jump parameters. Int. J. Control 72 (9), 842-850 (1999)
7. S. P. Boyd, L. E. Ghaoui, E. Feron, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)
8. ∞ control of uncertain Markovian jump systems with time-delay. IEEE Trans. Autom. Control 45, 77-83 (2000)
9. P. Dorato, Short time stability in linear time-varying systems, in Proc of the IRE International Convention Record, Part 4. New York (1961), pp. 83-87
10. ∞ control problems. IEEE Trans. Autom. Control 34, 831-847 (1989)
11. C. Gong, B. Su, Robust H-infinity filtering of convex polyhedral uncertain time-delay fuzzy systems. Int. J. Innov. Comput. Inf. Control 4 (4), 793-802 (2008)
12. ∞ state feedback control for generalized continuous/discrete time-delay system. Automatica 35, 1443-1451 (1999)
13. N. N. Krasovskii, E. A. Lidskii, Analytical design of controllers in systems with random attributes. Autom. Remote Control 22 (1) 1021-1025 (1961)
14. N. N. Krasovskii, E. A. Lidskii, Analytical design of controllers in systems with random attributes. Autom. Remote Control 22 (2) 1141-1146 (1961)
15. N. N. Krasovskii, E. A. Lidskii, Analytical design of controllers in systems with random attributes. Autom. Remote Control 22 (3) 1289-1294 (1961)
16. S. Limanond, J. Si, Neural-network-based control design: an LMI approach. IEEE Trans. Neural Netw. 9 (6), 1422-1429 (1998)
17. C. L. Lin, Control of perturbed systems using neural networks. IEEE Trans. Neural Netw. 9, 1046-1050 (1998)
18. ∞ design approach for neural net-based control schemes. IEEE Trans. Autom. Control 46, 1599-1605 (2001)
19. X. Mao, Stability of stochastic differential equations with Markovian switching. Stoch. Process. Appl. 79 (1), 45-67 (1999)
20. J. Qiu, H. Yang, P. Shi, Y. Xia, Robust H-infinity control for a class of discrete-time Markovian jump systems with time-varying delays based on delta operator. Circuits Syst. Signal Process. 27 (5), 627-643 (2008)
21. P. Shi, M. Mahmoud, J. Yi, A. Ismail, Worst case control of uncertain jumping systems with multistate and input delay information. Inf. Sci. 176 (2), 186-200 (2006)
22. C. E. Souza, D. F. Coutinho, Robust stability of a class of uncertain Markov jump nonlinear systems. IEEE Tran. Autom. Control 51 (11), 1825-1831 (2006)
23. J. A. K. Suykens, J. Vandewalle, B. D. Moor, Artificial Neural Networks for Modeling and Control of Non-linear Systems (Kluwer, Boston, 1996)
24. K. Tanaka, An approach to stability criteria of neural-network control systems. IEEE Trans. Neural Netw. 7 (3), 629-642 (1996) (Pubitemid 126776338)
25. Y. Wang, Z. Sun, H-infinity control of networked control system via LMI approach. Int. J. Innov. Comput. Inf. Control 3 (2), 343-352 (2007)
26. Y. Wang, L. Xie, C. E. de Souza, Robust control of a class of uncertain nonlinear systems. Syst. Control Lett. 19 (2), 139-149 (1992)
27. L. Weiss, E. F. Infante, Finite time stability under perturbing forces and on product spaces. IEEE Trans. Autom. Control 2 (2), 54-59 (1967)
28. M. Wu, F. Liu, P. Shi, Y. He, R. Yokoyama, Improved free-weighting matrix approach for stability analysis of discrete-time recurrent neural networks with time-varying delay. IEEE Trans. Circuits Syst. II, Express Briefs 55 (7), 690-694 (2008)
29. L. Wu, P. Shi, H. Gao, C. Wang, Robust H-infinity filtering for 2-D Markovian jump systems. Automatica 44 (7), 1849-1858 (2008)
30. L. Xia, M. Xia, L. Liu, LMI conditions for global asymptotic stability of neural networks with discrete and distributed delays. ICIC Express Lett. 2 (3), 257-262 (2008)
31. ∞ filtering for uncertain Markovian jump systems with modedependent time delays. IEEE Trans. Autom. Control 48 (5), 900-907 (2003)
32. J. Yi, G. Yang, Y. Zhu, Z. Tang, Dynamics analysis and a coefficient tuning method in a chaotic neural network. ICIC Express Lett. 2 (4), 323-330 (2008)