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[ $H_{\infty}$ ] Tracking Control of Time-delayed Linear Systems with Saturating Actuators  

Yi, Yearn-Gui (충북대학교 대학원 제어계측공학과)
Kim, Jin-Hoon (충북대학교 전기전자공학부)
Publication Information
The Transactions of The Korean Institute of Electrical Engineers / v.57, no.4, 2008 , pp. 668-676 More about this Journal
Abstract
In this paper, we considered the $H_{\infty}$ tracking control for time-delayed linear systems with saturating actuators. The considered time delay is a time varying one having bounded magnitude and rate, and the considered tracking reference is a general one only known its bounds of magnitude and rate. First, we have converted the $H_{\infty}$ tracking control problem into an equivalent $H_{\infty}$ disturbance attenuation problem using two steps of transformations. Next, based on a new Lyapunov-Krasovskii functional, we have derived the result in the form of LMI with two non-convex parameters. Finally, by numerical examples, we have shown the usefulness and effectiveness of our result.
Keywords
Time-delay; Actuator saturation; Lyapunov-Krasovskii function; LMI;
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Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By SCOPUS : 0
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1 E. Fridman, A. Pila and U. Shaked, "Regional stabilization and control of time-delay systems with saturating actuators," Int, J. Robust and Nonlinear Control, vol. 13, pp. 885-907, 2003   DOI   ScienceOn
2 Niculescu, S. -I., neto, A. T., Dion, J. -M., and Dugard, L., 1995 "Delay-Dependent Stability of Linear Systems with Delayed State: An LMI Approach," Proc. 34th IEEE Conf. on Decision and Control, pp. 1495-1497
3 S. Oucheriah, "Robust tracking and model following of uncertain dynamic systems by memoless linear controllers," IEEE Trans. Autom. Control, vol. 44, no. 7, pp. 1473-1577, July. 1999   DOI   ScienceOn
4 P. Park, "A delay-dependent stability criterion for system with uncertain time-invariant delays," IEEE. Trans. Autom. Control, vol. 44,no. 4,pp. 876-877, Apr, 1999   DOI   ScienceOn
5 S.-I. Niculescu, "Memoryless control with an -stability constrint for time-delay systems: An LMI approach," IEEE. Trans. Autom. Control, vol. 43,no. 5, pp. 739-743, May, 1998   DOI   ScienceOn
6 L. Zaccarian and A. R. Teel, "A common framework for anti-windup, bumpless transfer and reliable design," Automatica, vol. 38, pp. 1735-1744, 2002   DOI   ScienceOn
7 이연규, 김진훈, "제한된 구동기 용량을 갖는 시간지연 선형시스템의 제어," 전기학회 논문지, 56권, 9호, pp.1648-1654, 2007. 9   과학기술학회마을
8 T. Hu and Z. Lin, Control Systems with Actuator Saturation, Birkhauser, 2001
9 S. Tarbouriech and J. M. Gomes da Silva Jr, "Synthesis of controllers for continuous-time delay systems with saturating controls via LMI's," IEEE. Trans. Autom. Control, vol. 45, pp. 105-111, 2000   DOI   ScienceOn
10 H. Wu, "Adaptive robust tracking and model following of uncertain dynamical systems with multiple time delays," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 611-616, Apr. 2004   DOI   ScienceOn
11 W. J. Rogh, Linear System Theory. Upper Saddle River, New Jersey:Prentice Hall, 1996
12 H. Gao and C. Wang, "Delay-dependent robust and filtering for a class of uncertain nonlinear time-delay systems," IEEE. Trans. Autom. Control, vol. 48,no. 9, pp. 1661-1666, Sep, 2003   DOI   ScienceOn
13 X. Li and C. E. de Souza, "Delay-dependent robust stability and stabilization of uncertain linear delay systems: A linear matrix inequality approach," IEEE Trans. Autom. Control, vol. 42, no. 8,pp. 1144-1148, Aug. 1997   DOI   ScienceOn
14 J. -H. Kim and Z. Bien, "Robust stability of uncertain linear systems with saturating actuators," IEEE Trans. Autom. Control, vol. 39, pp. 202-207, 1994
15 Y. xia and Y. Jia, "Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals," Syst. Control Lett., vol. 50, pp. 183-193, 2003   DOI   ScienceOn
16 D. S. Bernstein and A. N. Michel(Eds), "Special issue:saturating actuator," Int, J. Robust and Nonlinear Control, vol. 5, pp. 375-540, 1995   DOI
17 E. Fridman and U. Shaked, "An improved stabilization method for linear time-delay systems," IEEE Trans. Autom. Control, vol. 47, no. 11,pp. 1931-1937, Nov. 2002   DOI   ScienceOn
18 S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA: SIAM, 1994
19 J. H. Kim, "Delay and its time-derivative dependent robust stability of time-delayed linear systems with uncertainty," IEEE. Trans. Autom. Control, vol. 46, no. 5, pp. 789-792, May, 2001   DOI   ScienceOn
20 Z. Lin and A. Saberi, "A semi-global low-and-high gain design technique for linear systems with input saturation-stabilization and disturbance rejection," Int, J. Robust and Nonlinear Control, vol. 5, pp. 381-398, 1995   DOI
21 M. Wu, Y. He, J. H. She and G. P. Liu "Delay-dependent criteria for robust stability of time-varying delay systems," Automatica, vol. 40, pp. 1435-1439, Mar, 2004   DOI   ScienceOn
22 P. O. Gutman and P. Hagander, "A new design of constrained controllers for linear systems," IEEE Trans. Autom. Contrl, vol. 30, pp. 22-33, 1985   DOI   ScienceOn