Robust mixed H2/Hinfin; delayed state feedback control of uncertain neutral systems with time-varying delays

Asian Journal of Control

Volumn 10, Issue 5, 2008, Pages 569-580

  Karimi, Hamid Reza ^a,b,c   Zapateiro, Mauricio ^b,c   Luo, Ningsu ^b,c  

^a Center of Excellence Development and Strategic Plants for Bioprocess Technology   (Iran)

^b UNIVERSITY OF TEHRAN   (Iran)

^c UNIVERSITY OF GIRONA   (Spain)

Author keywords

Linear matrix inequalities; Mixed H2 Hinfin; control; Neutral systems; Time delay; Uncertainty

Indexed keywords

CLOSED LOOP SYSTEMS; CONVEX OPTIMIZATION; DELAY CONTROL SYSTEMS; FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; ROBUST CONTROL; STABILIZATION; STATE FEEDBACK; TIME DELAY; TIME VARYING CONTROL SYSTEMS;

CONVEX OPTIMIZATION METHODS; DELAYED STATE FEEDBACK; DISCRETE AND DISTRIBUTED DELAYS; LYAPUNOV-KRASOVSKII FUNCTIONALS; NEUTRAL SYSTEMS; STABILITY AND STABILIZATIONS; UNCERTAIN NEUTRAL SYSTEMS; UNCERTAINTY;

DISCRETE TIME CONTROL SYSTEMS;

EID: 56249089673     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1002/asjc.57     Document Type: Article

References (36)

1. Niculescu, S. I., E. I. Verriest, L. Dugard, and J. M. Dion, " Stability and robust stability of time-delay systems: A guided tour " in: L. Dugard. et al., (Eds), Stability and Control of Time-Delay Systems. Springer: Berlin, Germany, Vol. 228, pp. 1-71 (1998).
2. Malek-Zavarei, M. and M. Jamshidi, Time-delay Systems: Analysis, Optimisation and Application, North-Holland, Amsterdam (1987).
3. Niculescu, S. I., Delay Effects on Stability: A Robust Control Approach, Springer, Berlin (2001).
4. Mac-Donald, N., Biological Delay systems: Linear Stability Theory, Cambridge University Press, Cambridge, (1989).
5. Kuang Y., Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston, (1993).
6. He, Y., M. Wu, J. H. She, and G. P. Liu, " Delay-dependent robust stability criteria for uncertain neutral systems with mixed delays, " Syst. Control Lett., Vol. 51, pp. 57-65 (2004).
7. Han, Q. L., " A descriptor system approach to robust stability of uncertain neutral systems with discrete and distributed delays, " Automatica, Vol. 40, pp. 1791-1796(2004).
8. He, Y, Q. G. Wang, C. Lin, and M. Wu, " Delay-range-dependent stability for systems with time-varying delay, " Automatica, Vol. 43, pp. 371-376 (2007).
9. Gu K., " An integral inequality in the stability problem of time-delay systems, " Proc. 39th IEEE Conf. Decis. Control, Sydney, pp. 2805-2810 (2000).
10. Krasovskii, N. N., Stability of Motion, Stanford University Press, Stanford, CA (1963).
11. Han, C. L. and L. Yu, " Robust stability of linear neutral systems with nonlinear parameter perturbations, " IEEE Proc. Control Theory Appl., Vol. 151, No. 5, pp. 539-546 (2004).
12. infin; model reduction of linear systems with distributed delay, " IEEE Proc. Control Theory Appl, Vol. 152, No. 6, pp. 662-674 (2005).
13. Fridman, E., " New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems, " Syst. Control Lett., Vol. 43, pp. 309-319(2001).
14. Hu, G. D., " Some simple stability criteria of neutral del ay-differential systems, " Appl. Math. Comput., Vol. 80, pp. 257-271 (1996).
15. Chen, W. H. and W. X. Zheng, " Delay-dependent robust stabilization for uncertain neutral systems with distributed delays, " Automatica, Vol. 43, pp. 95-104 (2007).
16. Chen, J. D., C. H. Lien, K. K. Fan, and J. H. Chou, " Criteria for asymptotic stability of a class of neutral systems via a LMI approach, " IEEE Proc. Control Theory Appl, Vol. 148, pp. 442-447 (2001).
17. infin; control of uncertain neutral systems with state and input delays, " J. Optim. Theory Appl, Vol. 126, pp. 553-570 (2005).
18. infin; control: constant and time-varying delays, " Int. J. Control, Vol. 76, pp. 48-60 (2003).
19. infin; control of linear time-delay systems ," IEEE Trans. Autom. Control, Vol. 48, pp. 520-525 (2003).
20. infin; control of linear neutral systems, " Automatica, Vol. 36, pp. 757-764 (2000).
21. infin; and positive-real control for linear neutral delay systems, " IEEE Trans. Autom. Control, Vol. 46, pp. 1321-1326 (2001).
22. infin; controller of uncertain neutral systems with discrete and distributed time-varying delays, " J. Optim. Theory Appl, Vol. 131, No. 3, pp. 383-403 (2006).
23. infin; control for uncertain linear neutral delay systems, " Optim. Control Appl Methods, Vol. 23, pp. 113-123 (2002).
24. Xu, S., Y Chu, J. Lu, and Y Zou, " Exponential dynamic output feedback controller design for stochastic neutral systems with distributed delays, " IEEE Trans. Syst, Man, Cybern. A: Syst. Hum., Vol. 36, pp. 540-548 (2006).
25. Chen, B., J. Lam, and S. Xu, " Memory state feedback guaranteed cost control for neutral systems, " Int. J. Innov. Comp. Inf. Control, Vol. 2, No. 2, pp. 293-303 (2006).
26. Lien, C. H., " Guaranteed cost observer-based controls for a class of uncertain neutral time-delay systems, " J. Optim. Theory Appl, Vol. 126, No. 1, pp. 137-156 (2005).
27. Park, J. H., " Guaranteed cost stabilization of neutral differential systems with parametric uncertainty, " J. Comput. Appl. Math., Vol. 151, pp. 371-382 (2003).
28. Xu, S., J. Lam, C. Yang, and E. I. Verriest, " An LMI approach to guaranteed cost control for uncertain linear neutral delay systems, " Int. J. Robust Nonlinear Control, Vol. 13, pp. 35-53 (2003).
29. Fiagbedzi, Y and A. Pearson, " A multistage reduction technique for feedback stabilizing distributed time-lag systems, " Automatica, Vol. 23, pp. 311-326(1987).
30. Wang, Y, L. Xie, and C. E. de Souza, " Robust control for a class of uncertain nonlinear systems, " Syst. Control Lett., Vol. 19, pp. 139-149 (1992).
31. Park, P., " A delay-dependent stability criterion for systems with uncertain time-invariant delays, " IEEE Trans. Autom. Control, Vol. 44, pp. 876-877 (1999).
32. infin; control for uncertain systems with a state-delay, " Automatica, Vol. 40, pp. 65-72 (2004).
33. Ivanescu, D., S. I. Niculescu, L. Dugard, J. M. Dion, and E. I. Verriest, " On delay-dependent stability for linear neutral systems, " Automatica, Vol. 39, pp. 255-261 (2003).
34. Kolmanovskii, V. B. and A. Myshkis, Applied Theory of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht (1992).
35. Gahinet, P, A. Nemirovsky, A. J. Laub, and M. Chilali, LMI Control Toolbox: For Use with Matlab, The MathWorks, Inc.: Natick, MA (1995).
36. Boyd, S., E. L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Mathematics, SIAM: Philadelphia, PA (1994).