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Dissipativity Analysis and Synthesis of Singular Systems via Delta Operator Method

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Proceedings of the 2015 Chinese Intelligent Automation Conference

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 337))

Abstract

This paper investigates the problems of dissipativity analysis and synthesis for singular systems through delta operator method. First, a sufficient condition is obtained such that a singular delta operator system is admissible and strictly dissipative. Then the existence condition and explicit expression of a state feedback strictly dissipative controller are presented. A numerical example is also provided to demonstrate the effectiveness of the theoretical results.

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References

  1. Dai L (1989) Singular control systems. Springer-Verlag, Berlin

    Book  MATH  Google Scholar 

  2. Dong X (2007) Robust strictly dissipative control for discrete singular system. IET Control Theory Appl 1(4):1060–1067

    Article  MathSciNet  Google Scholar 

  3. Dong X (2014) Admissibility analysis of linear singular systems via a delta operator method. Int J Syst Sci 45(11):2366–2375

    Article  Google Scholar 

  4. Dong X, Tian W, Mao Q et al (2013) Robust admissibility analysis and synthesis of uncertain singular systems via delta operator approach. In: 10th IEEE international conference on control & automation, Hangzhou, China, pp 1059–1064

    Google Scholar 

  5. Duan G, Yu H, Wu A et al (2012) Analysis and design of descriptor linear systems. Science Press, Beijing

    Google Scholar 

  6. Goodwin GC, Lozano Leal R, Mayne DQ, Middleton RH (1986) Rapproachement between continuous and discrete model reference adaptive control. Automatica 22(2):199–207

    Google Scholar 

  7. Li G, Gevers M (1993) Comparative study of finite wordlength effects in shift and delta operator parameterizations. IEEE Trans Autom Control 38(5):803–807

    Article  MATH  MathSciNet  Google Scholar 

  8. Liu L, Dong X, Wang W (2011) Robust strict dissipativeness analysis for affinely uncertain singular systems. In: 2011 IEEE 5th international conference on cybernetics and intelligent systems, Qingdao, China, pp 81–86

    Google Scholar 

  9. Liu L, Dong X, Wang W (2011) State feedback robust dissipative control for singular systems with affine uncertainty. In: 2011 IEEE 5th international conference on cybernetics and intelligent systems, Qingdao, China, pp 99–104

    Google Scholar 

  10. Mao Q, Dong X, Tian W (2012) Admissibility conditions for linear singular delta operator systems: analysis and synthesis. In: Proceedings of the 10th world congress on intelligent control and automation. Beijing, China, pp 1870–1875

    Google Scholar 

  11. Middleton R, Goodwin GC (1986) Improved finite word length characteristics in digital control using delta operators. IEEE Trans Autom Control 31(11):1015–1021

    Article  MATH  Google Scholar 

  12. Willems JC (1972) Dissipative dynamical systems—part 1: general theory. Arch Ration Mech Anal 45(5):321–351

    Article  MATH  MathSciNet  Google Scholar 

  13. Willems JC (1972) Dissipative dynamical systems—part 2: linear systems with quadratic supply rates. Arch Ration Mech Anal 45(5):352–393

    Article  MATH  MathSciNet  Google Scholar 

  14. Wu J, Li G, Istepanian RH, Chu J (2000) Shift and delta operator realisation for digital controllers with finite word length consideration. IEEE Proc Control Theory Appl 147(6):664–672

    Article  Google Scholar 

  15. Xu S, Lam J (2006) Robust control and filtering of singular systems. Springer, Berlin

    MATH  Google Scholar 

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Acknowledgments

This work is supported by National Natural Science Foundation of China under Grant 61104001.

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Correspondence to Xin-zhuang Dong .

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Qi, Cm., Dong, Xz., Liu, L. (2015). Dissipativity Analysis and Synthesis of Singular Systems via Delta Operator Method. In: Deng, Z., Li, H. (eds) Proceedings of the 2015 Chinese Intelligent Automation Conference. Lecture Notes in Electrical Engineering, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46463-2_3

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  • DOI: https://doi.org/10.1007/978-3-662-46463-2_3

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46462-5

  • Online ISBN: 978-3-662-46463-2

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