Global stabilization of the double integrator system with saturation and delay in the input

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 57, Issue 6, 2010, Pages 1371-1383

  Zhou, Bin ^a   Duan, Guangren ^a   Lin, Zongli ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b University of Virginia   (United States)

Author keywords

Actuator saturation; Global stabilization; Linear feedback; Nonlinear systems; Time delay

Indexed keywords

ACTUATOR SATURATIONS; DELAY INDEPENDENT; DELAY-DEPENDENT; DOUBLE INTEGRATOR; FEEDBACK DESIGNS; FREE PARAMETERS; GLOBAL STABILIZATION; GLOBALLY ASYMPTOTICALLY STABLE; LINEAR FEEDBACK; LINEAR STATE FEEDBACK; NUMERICAL EXAMPLE; PARAMETERIZED;

ACTUATORS; FEEDBACK; NONLINEAR FEEDBACK; NONLINEAR SYSTEMS; STABILIZATION; TIME DELAY;

STATE FEEDBACK;

EID: 77953480746     PISSN: 15498328     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2009.2028645     Document Type: Article

References (45)

1. M. Athans and P. L. Falb, Optimal Control: An Introduction to the Theory and Applications. New York: McGraw Hill, 1966.
2. A. Benzaouia and F. Mesquine, The regulator problem for linear systems with saturations on the control and its increments or rate: An LMI approach, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.53, no.12, pp. 2681-2691, Dec. 2006.
3. Y. Cao, Z. Lin, and T. Hu, Stability analysis of linear time-delay systems subject to input saturation, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.49, no.2, pp. 233-240, Feb. 2002. (Pubitemid 34291474)
4. A. Cepeda and A. Astolfi, Control of a planar system with quantized and saturated input/output, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.55, no.3, pp. 932-942, Mar. 2008.
5. M. Chen and G. Feng, Delay-dependent H∞ filtering of piecewise- linear systems with time-varying delays, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.55, no.7, pp. 2087-2096, Jul. 2008.
6. W. Chen and W. Zheng, Global exponential stability of impulsive neural networks with variable delay: An LMI approach, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.56, no.6, pp. 1248-1259, Jun. 2009.
7. Y. Chitour, On the Lp stabilization of the double integrator subject to input saturation, in Proc. ESAIM: Control, Opt. Calculus Variations, 2001, vol.6, pp. 291-331.
8. H. Fang and Z. Lin, A further result on global stabilization of oscillators with bounded delayed input, IEEE Trans. Autom. Control, vol.51, no.1, pp. 121-128, Jan. 2006.
9. H. Fang and Z. Lin, Global practical stabilization of planar linear systems in the presence of actuator saturation and input additive disturbance, IEEE Trans. Autom. Control, vol.51, no.7, pp. 1177-1184, Jul. 2006.
10. K. Gu, V. Kharitonov, and J. Chen, Stability of Time-Delay Systems. Boston, MA: Birkhauser, 2003.
11. T. Gustafsson, On the design and implementation of a rotary crane controller, Eur. J. Control, vol.2, pp. 166-175, 1996.
12. J. K. Hale and S. M. V. Lunel, Introduction to Functional Differential Equations, Applied Mathematical Sciences. New York: Springer, 1993, vol.99.
13. Q. Han, On designing time-varying delay feedback controllers for master-slave synchronization of Lur'e systems, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.54, no.7, pp. 1573-1583, Jul. 2007. (Pubitemid 47104021)
14. Y. Hong, J. Huang, and Y. Xu, On an output feedback finite-time stabilization problem, IEEE Trans. Autom. Control, vol.46, no.2, pp. 305-309, Feb. 2001.
15. T. Hu and Z. Lin, A complete stability analysis of planar linear systems under saturation, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.47, no.4, pp. 498-512, Apr. 2000.
16. T. Huand Z. Lin, A complete stability analysis of planardiscrete-time linear systems under saturation, IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol.48, no.6, pp. 710-725, Jun. 2001. (Pubitemid 32609775)
17. T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design. Boston, MA: Birkhauser, 2001.
18. L. Huang, X. Mao, and F. Deng, Stability ofhybrid stochastic retarded systems, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.55, no.11, pp. 3413-3420, Nov. 2008.
19. P. C. Hughes, Spacecraft Attitude Dynamics. New York: Wiley, 1986.
20. W. Jing and C. R. Mclnnes, Memorised quasi-time-fuel-optimal feedback control of perturbed double integrator, Automatica, vol.38, pp. 1389-1396, 2002.
21. S. Kim, S. Campbell, and X. Liu, Stability of a class of linear switching systems with time delay, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.53, no.2, pp. 384-393, Feb. 2006.
22. S. Kuo, H. Wu, and F. Chen, Saturation effects in active noise control systems, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.51, no.6, pp. 1163-1171, Jun. 2004.
23. Z. Lin and H. Fang, On asymptotic stabilizability of linear systems with delayed input, IEEE Trans. Autom. Control, vol.52, no.6, pp. 998-1013, Jun. 2007.
24. Z. Lin and A. Saberi, Semi-global exponential stabilization of linear systems subject to 'input saturation' via linear feedbacks, Syst. Control Lett., vol.21, no.3, pp. 225-239, 1993.
25. T. Liu, X. He, D. Y. Gu, and W. D. Zhang, Analytical decoupling control design for dynamic plants with time delay and double integrators, IEE Proc.-Control Theory Appl., vol.151, no.6, pp. 745-753, 2004.
26. X. Liu, X. Shen, and Y. Zhang, Stability criteria for impulsive systems with time delay and unstable system matrices, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.54, no.10, pp. 2288-2298, Oct. 2007. (Pubitemid 350141874)
27. H. Lu, J. Gao, and D. W. C. Ho, Adaptive stabilization and synchronization for chaotic Lur'e systems with time-varying delay, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.55, no.5, pp. 1347-1356, 2008.
28. N. Marchand and A. Hably, Global stabilization of multiple integrators with bounded controls, Automatica, vol.41, no.12, pp. 2147-2152, 2005.
29. F. Mazenc, S. Mondie, and S.-I. Niculescu, Global asymptotic stabilization for chains of integrators with a delay in the input, IEEE Trans. Autom. Control, vol.48, no.1, pp. 57-63, Jan. 2003.
30. F. Mazenc, S. Mondie, and S.-I. Niculescu, Global stabilization of oscillators with bounded delayed input, Syst. Control Lett., vol.53, no.5, pp. 415-422, 2004.
31. V. G. Rao and D. S. Berstein, Naive control of the double integrator, IEEE Trans. Control Syst. Mag., vol.21, no.5, pp. 86-97, Sep. 2001.
32. G. Shi and A. Saberi, On the input-to-state stability (ISS) of a double integrator with saturated linear control laws, in Proc. Amer. Control Conf., 2002, pp. 59-61.
33. O. J. M. Smith, A controller to overcome dead time, ISA J. Instrument Soc. Amer., vol.6, pp. 28-33, 1959.
34. A. A. Stoorvogel, G. Shi, and A. Saberi, External stability of a double integrator with saturated linear control laws, Dyn. Continuous, Discrete Impulsive Syst., vol.11, no.4-5, pp. 429-451, 2004.
35. S. Tarbouriech, G. Garcia, and A. H. Glattfelder, Eds., Advanced Strategies in Control Systems with Input and Output Constraints, in: LNCIS. New York: Springer-Verlag, 2007, vol.346.
36. A. R. Teel, Global stabilization and restricted tracking for multiple integrators with bounded controls, Syst. Control Lett., vol.18, no.3, pp. 165-171, 1992.
37. F. Tyan and D. S. Bernstein, Global stabilization of systems containing a double integrator using a saturated linear controller, Int. J. Robust Nonlinear Control, vol.9, pp. 1143-1156, 1999.
38. Z. Wen, S. Roy, and A. Saberi, On the disturbance response and external stability of a saturating static -feedback-controlled double integrator, Automatica, vol.44, no.8, pp. 2191-2196, 2008.
39. S. Xu, J. Lam, and C. Yang, Quadratic stability and stabilization of uncertain linear discrete-time systems with state-delay, Syst. Control Lett., vol.43, pp. 77-84, 2001.
40. S. Xu, J. Lam, and X. Mao, Delay-dependent Woo control and filtering for uncertain markovian jump systems with time-varying delays, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.54, no.9, pp. 2070-2077, Sep. 2007.
41. K. Yakoubi and Y. Chitour, Linear systems subject to input saturation and time delay: Global asymptotic stabilization, IEEE Trans. Autom. Control, vol.52, no.5, pp. 874-879, May 2007.
42. H. Zhang, D. Zhang, and L. Xie, An innovation approach to H∞ prediction with applications to systems with delayed measurements, Automatica, vol.40, no.7, pp. 1253-1261, 2004.
43. M. Zhong and Q. L. Han, Fault-tolerant master - slave synchronization for Lur'e systems using time-delay feedback control, IEEE Trans. Circuits Syst. I, Reg. Papers, vol.56, no.7, pp. 1391-1404, Jul. 2009.
44. B. Zhou, G.-R. Duan, and Z. Lin, A parametric Lyapunov equation approach to the design of the low gain feedback, IEEE Trans. Autom. Control, vol.53, no.6, pp. 1548-1554, Jul. 2008.
45. B. Zhou, G.-R. Duan, and Li Z.-Y, On improving transient performance in global control of multiple integrators system by bounded feedback, Syst. Control Lett., vol.57, no.10, pp. 867-875, 2008.