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Mixed L 1/H-infinity control for uncertain linear singular systems

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Abstract

The mixed L 1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L 1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and *-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.

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References

  1. J. C. Doyle, B. A. Francis, A. R. Tannenbanum. Feedback Control Theory[M]. New York: Maxwell Macmillan International, 1992.

    Google Scholar 

  2. G. Zames. Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms and approximate inverses[J]. IEEE Transactions on Automatic Control, 1981, 26(2): 301–320.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. C. Youla, H. A. Jabr, J. J. Bongiorno. Modern Wiener-Hopf design of optimal controllers — Part II: the multi-variables cases[J]. IEEE Transactions on Automatic Control, 1976, 21(3): 319–338.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. E. Barabanov, O. N. Granichin. An optimal controller for linear plant with bounded noises[J]. Automatica, 1984, 5(2): 41–46.

    Google Scholar 

  5. M. Vidyasagar. Optimal rejection of persistent bounded disturbances[J]. IEEE Transactions on Automatic Control, 1986, 31(6):527–534.

    Article  MATH  MathSciNet  Google Scholar 

  6. I. Kaminer, P. P. Khargonekar, M. A. Rotea. Mixed H2/H∞ control for discrete time systems via convex optimization[J]. Automatica, 1993, 29(1): 57–70.

    Article  MATH  MathSciNet  Google Scholar 

  7. M. Sznaier, J. Bu. On the properties of the solutions to mixed l 1/H∞ control problems[C]//Proceedings of the 13th IFAC Congress. Oxford: Pergamon Press, 1996: 249–254.

    Google Scholar 

  8. M. V. Salapaka, M. Dahleh, P. Voulgaris. Mixed objective control synthesis control: optimal l 1/H2 control[J]. SIAM Journal of Control and Optimization, 1997, 35(5): 1672–1689.

    Article  MATH  MathSciNet  Google Scholar 

  9. L. Dai. Singular Control Systems[M]. Berlin: Springer-Verlag, 1989.

    Google Scholar 

  10. D. J. Bender, A. J. Laub. The linear quadratic optimal regulator for descriptor systems[J]. IEEE Transactions on Automatic Control, 1987, 32(8): 672–688.

    Article  MATH  MathSciNet  Google Scholar 

  11. S. Xu, C. Yang, Y. Niu, et al. Robust stabilization for uncertain discrete singular systems[J]. Automatica, 2001, 37(5): 769–774.

    MATH  MathSciNet  Google Scholar 

  12. I. Masubuchi, Y. Kamitae, A. Ohara, et al. H∞ control for descriptor systems: a matrix inequalities approach[J]. Automatica, 1997, 33(4):669–673.

    Article  MATH  MathSciNet  Google Scholar 

  13. X. Wang. Optimizing Design of Fixed-order L 1 Controller[D]. Zhejiang: Zhejiang University Publishing House, 2006.

    Google Scholar 

  14. X. Ji, Y. Sun. Robust L 1 control for uncertain linear singular systems: a matrix inequality approach[C]//Proceedings of the 3rd International Conference on Impulsive Dynamic Systems and Applications. Waterloo: Watam Press, 2006: 450–453.

    Google Scholar 

  15. J. Abedor, K. Nagpal, K. Poolla. A linear matrix inequality approach to peak-to-peak gain minimization[J]. International Journal of Robust and Nonlinear Control, 1996, 6(9): 899–927.

    Article  MATH  MathSciNet  Google Scholar 

  16. I. R. Petersen. A stabilization algorithm for a class of uncertain linear systems[J]. Systems & Control Letters, 1987, 8(4): 351–357.

    Article  MATH  MathSciNet  Google Scholar 

  17. L. Zhang, B. Huang. LMI synthesis of H2 and mixed H2/H∞ controllers for singular systems[J]. IEEE Transactions on Automatic Control, 2003, 50(9): 615–626.

    Google Scholar 

  18. S. Boyd, L. EI. Ghaoui, E. Feron, et al. Linear Matrix Inequalities in System and Control Theory[M]. Philadelphia: SIAM, 1994.

    Google Scholar 

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Authors and Affiliations

  1. School of Electrical and Information Engineering, Jiangsu University, Zhenjiang, Jiangsu, 212013, China

    Xiaofu Ji, Yukun Sun & Yonghong Huang

  2. National Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    Hongye Su

Authors
  1. Xiaofu Ji
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  2. Yukun Sun
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  3. Yonghong Huang
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  4. Hongye Su
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Corresponding author

Correspondence to Xiaofu Ji.

Additional information

This work was supported by the National Natural Science Foundation of China (No.60774044), the Professional Research Foundation for Advanced Talents of Jiangsu University (No.07JDG037), the Natural Science Fund for Colleges and Universities in Jiangsu Province (No.08KJ510010), the Open Project of National Key Laboratory of Industrial Control Technology of Zhejiang University (No.ICT0910), and Qing Lan Project of Jiangsu Province.

Xiaofu JI received the M.S. degree from Jiangsu University and the Ph.D. degree from Zhejiang University in 2003 and 2006, respectively, both in Control Theory and Applications. Now, he is a lecturer in Jiangsu University. His research interests include robust control and filtering, singular linear systems and saturated control.

Yukun SUN received the Ph.D. degree from Jiangsu University in 2006. Now, he is a professor at Jiangsu University. His research interests include motion control, robust control and power systems.

YongHong HUANG received the M.S. degree from Jiangsu University in 1996. Now, he is an associate professor at Jiangsu University. His research interests include motion control, robust control and power systems.

Hongye SU was born in Jiangsu, China, in 1969. He received a first class B.S. degree in Industrial Automation from Nanjin University of Chemical Technology in 1990. He later obtained the M.S. and Ph.D. degrees from Zhejiang University in 1993 and 1995, respectively. He is currently a professor at the Institute of Advanced Process Control, Zhejiang University. His recent research interests include robust control, time-delay systems, advanced process control theory and application.

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Ji, X., Sun, Y., Huang, Y. et al. Mixed L 1/H-infinity control for uncertain linear singular systems. J. Control Theory Appl. 7, 134–138 (2009). https://doi.org/10.1007/s11768-009-7169-4

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  • DOI: https://doi.org/10.1007/s11768-009-7169-4

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