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http://dx.doi.org/10.5302/J.ICROS.2007.13.6.581

Guaranteed Cost Control for Uncertain Time-Delay Systems with nonlinear Perturbations via Delayed Feedback  

Park, Ju-Hyun (영남대학교 전기공학과)
Kwon, Oh-Min (충북대학교 전기공학과)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.13, no.6, 2007 , pp. 581-588 More about this Journal
Abstract
In this paper, we propose a delayed feedback guaranteed cost controller design method for linear time-delay systems with norm-bounded parameter uncertainties and nonlinear perturbations. A quadratic cost function is considered as the performance measure for the given system. Based on the Lyapunov method, an LMI optimization problem is formulated to design a controller such that the closed-loop cost function value is not more than a specified upper bound for all admissible system uncertainties and nonlinear perturbations. Numerical example show the effectiveness of the proposed method.
Keywords
delay; guaranteed cost control; LMI; Lyapunov method; nonlinear perturbations; uncertain time-delay systems;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 O. Kwon, S. Won, and D. Yue, 'Delayed feedback guaranteed cost controller design for uncertain time-delay systems,' IEICE Trans. Fundamentals, vol. E86-A, no. 9, 2413-2417, 2003
2 Z. Zuo and Y. Wang, 'New stability criterion for a class of linear systems with time-varying delay and nonlinear perturbations,' IEE Proceedings-Control Theory and Applications, vol. 153, no. 5, pp. 623-626, 2006   DOI   ScienceOn
3 Y. S. Lee, O. K. Kwon, and W. H. Kwon, 'Delay-dependent guaranteed cost control for uncertain state-delayed systems,' lnternational Journal of Control, Automation, and Systems, vol. 3, no. 4, pp. 524-532, 2005
4 W. H. Chen, Z. H. Guan, and X. M. Lu, 'Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays,' Journal of the Franklin Institute. vol. 341. no. 5, pp. 419-430, 2004   DOI   ScienceOn
5 W. H. Chen, Z. H. Guan, and X. M. Lu, 'Delay-dependent guaranteed cost control for uncertain discrete-time systems with delay,' IEE Proceedings-Control Theory and Applications, vol. 150, no. 4, pp. 412-416, 2003   DOI   ScienceOn
6 W. H. Chen, Z. H. Guan, and X. M. Lu, 'Delay-dependent output feedback guaranteed cost control for uncertain time-delay systems,' Automatica, vol. 40, no. 7, pp. 1263-1268, 2004   DOI   ScienceOn
7 O. M. Kwon, J. H. Park, S. M. Lee, and S. C. Won, 'LMI optimization approach to observer-based controller design of uncertain time-delay systems via delayed feedback,' Journal of Optimization Theory and Applications, vol. 128, no. 1, pp. 103-107, 2006   DOI
8 P. Gahinet, A. Nemirovskii, A. Laub, and M. Chilali, LMI Control Toolbox, Math Works, Natick, Massachusetts, 1995
9 X. M. Zhang, M. Wu, J. H. She, and Y. He, 'Delay-dependent stabilization of linear systems with time-varying state and input delays,' Automatica, vol. 41, pp. 1405-1412, 2005   DOI   ScienceOn
10 Y. S. Moon, P. Park, and W. H. Kwon, 'Robust stabilization of uncertain input-delayed systems using reduction method,' Automatica, vol. 37, pp. 307-312, 2001   DOI   ScienceOn
11 Z. H. Gua, C. W. Chan, Andrew Y. T. Leung, and G. Chen, 'Robust stabilization of singular-impulsive-delayed systems with nonlinear perturbations,' IEEE Trans. On Circuits and Systems-I: Fundamental Theory and Applications, vol. 48, no. 8, pp. 1011-1019, 2001   DOI   ScienceOn
12 Y. S. Lee, Y. S. Moon, and W. H. Kwon, 'Delay-dependent guaranteed cost control for uncertain state-delayed systems,' Proceedings of the American Control Conference, pp. 3376-3381, 2001   DOI
13 Y. H. Roh and J. H. Oh, 'Robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation,' Automatica, vol. 35, pp. 1861-1865, 1999   DOI   ScienceOn
14 S. S. L. Chang and T. K. C. Peng, 'Adaptive guaranteed cost control of systems with uncertain parameters,' IEEE Trans. On Automatic Control, vol. 17, no. 4, pp. 474-483, 1972   DOI
15 O. M. Kwon and J. H. Park, 'An improved delay-dependent robust control for uncertain time-delay systems,' IEEE Trans. On Automatic Control, vol. 49, no. 11, pp, 1991-1995, 2004   DOI   ScienceOn
16 T. Mori, 'Criteria for asymptotic stability of linear time-delay systems,' IEEE Trans. On Automatic Control, vol. 30, no. 2, pp. 158-161, 1985   DOI   ScienceOn
17 S. H. Esfahani and I. R. Peterson, 'An LMI approach to output-feedback guaranteed cost control for uncertain time-delay systems,' International Journal of Robust and Nonlinear Control, vol. 10, pp. 157-174, 2000   DOI   ScienceOn
18 S. Oucherich, 'Global stabilization of a class of linear continuous time-delay systems with saturating controls,' IEEE Trans. On Circuits and Systems-I : Fundamental Theory and Applications, vol. 43, no. 12, pp. 1012-1015, 1996   DOI   ScienceOn
19 O. M. Kwon and J. H. Park, 'Robust stabilization of uncertain systems with delays in control input,' Applied Mathematics and Computation, vol. 172, pp. 1067-1077, 2006   DOI   ScienceOn
20 L. Yu and J. Chu, 'An LMI approach to guaranteed cost control of linear uncertain time-delay systems,' Automatica, vol. 35, pp. 1155-1159, 1999   DOI   ScienceOn
21 L. Yu and F. Gao, 'Optimal guaranteed cost control of discrete-time uncertain systems with both state and input delays,' Journal of the Franklin Institute, vol. 338, pp. 101-110, 2001   DOI   ScienceOn
22 K. Gu, 'A further refinement of discretized Lyapunov functional method for the stability of time-delay systems,' International Journal of Control, vol. 74, no. 10, pp. 967-976, 2001   DOI
23 D. Yue and S. Won, 'Delay-dependent robust stability of stochastic systems with time delay and nonlinear uncertainties.' Electronics Letters, vol. 37, pp. 992-993, 2001   DOI   ScienceOn
24 K. Gu and S.-I. Niculescu, 'Further remarks on additional dynamics in various model transformations of linear delay systems,' IEEE Trans. On Automatic Control, vol. 46, no. 3, pp. 497-500, 2001   DOI   ScienceOn
25 J. H. Kim, 'Robust guaranteed cost control of discrete-time uncertain systems,' IEICE Trans. Fundamentals, vol. E84-A, no. 8, pp. 2065-2069, 2001
26 K. Gu, 'An integral inequality in the stability of time-delay Systems,' IEEE Conference on Decision and Control, Sydney, Australia, 2000   DOI
27 J. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Springer-Verlag, New York, 1993
28 S. Boyd, L. El Ghaoui, E. Feron, and V. balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia, 1994
29 C. Gouding, Y. Maying, L. Yu, and C. Jian, 'Delay dependent guaranteed cost control for linear uncertain time-delay systems,' Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, P.R. China, pp. 3363-3367, 2000   DOI