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Stabilization Design for Uncertain Linear Positive Systems with Time-Delay

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Positive Systems (POSTA 2018)

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 480))

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Abstract

Stabilization design for a class of uncertain linear positive systems with time-delay is devoted in this paper. By using the theory of positive system and the theorem of disk region, the interval observer is designed. And a control law is acquired based on the state of interval observer. Then, it is proved that the control law such that the closed-loop system is positive and asymptotically stable. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.

This work is supported by the National Natural Science Foundation of China (61773350, 61473265, 11671361) and the Natural Science Foundation of Zhejiang Province of China (LY17F030001).

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References

  1. Busowicz, M.: Robust stability of positive discrete-time linear systems of fractional order. Bull. Pol. Acad. Sci, Tech. Sci. 58, 567–572 (2010)

    Google Scholar 

  2. Efimov, D., Rassi, T., Zolghadri, A.: Control of nonlinear and LPV systems: interval observer-based framework. IEEE Trans. Autom. Control 58, 773–778 (2013)

    Article  MathSciNet  Google Scholar 

  3. Garcia, G., Bernussou, J.: Pole assignment for uncertain systems in a specified disk by state feedback. IEEE Trans. Autom. Control 40, 184–190 (1995)

    Article  MathSciNet  Google Scholar 

  4. Gouz, J., Rapaport, A., Hadj-Sadok, M.: Interval observers for uncertain biological systems. Ecol. Model. 133, 45–56 (2000)

    Article  Google Scholar 

  5. Haddad, W., Chellaboina, V.: Stability theory for nonnegative and compartmental dynamical systems with time delay. In: Proceedings of the 2004 American Control Conference, pp. 1422–1427 (2004)

    Google Scholar 

  6. Li, Y., Jian, C.: An LMI approach to guaranteed cost control of linear uncertain time-delay systems. Automatica 35(6), 1155–1159 (1999)

    Article  MathSciNet  Google Scholar 

  7. Li, Z.B., Zhu, S.Q.: Resilient static output feedback stabilization for controlled positive time-delay systems. J. Shandong Univ. (Eng. Sci.) 41, 46–51 (2011)

    Google Scholar 

  8. Li, T., Zhang, H.X., Sun, P.: New criterion of robust stability for interval time-varying delays linear uncertain systems. Control. Decis. 25(6), 953–957 (2010)

    MathSciNet  Google Scholar 

  9. Liu X.W., Zhong S.M.: Stability analysis of positive systems with unbounded delays. In: Chinese Control and Decision Conference, pp. 193–198 (2010)

    Google Scholar 

  10. Liu, X.W., Yu, W.S., Wang, L.: Stability analysis of positive systems with bounded time-varying delays. IEEE Trans. Circuits Syst II: Expr Briefs 56, 600–604 (2009)

    Article  Google Scholar 

  11. Liu, X.W., Yu, W.S., Wang, L.: Stability analysis for continuous-time positive systems with time-varying delays. IEEE Trans. Autom. Control 55, 1024–1028 (2010)

    Article  MathSciNet  Google Scholar 

  12. Qu, Z.H.: Robust control of a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 37(9), 1437–1442 (1992)

    Article  Google Scholar 

  13. Rami, M., Helmke, U., Tadeo, F.: Positive observation problem for linear time-lag positive systems. IFAC Proc. Vol. 40, 536–541 (2007)

    Article  Google Scholar 

  14. Rami M., Helmke U., Tadeo F.: Positive observation problem for linear time-delay positive systems. In: 2007 Mediterranean Conference on Control Automation, pp. 1–6 (2007)

    Google Scholar 

  15. Shu, Z., Lam, J., Gao, H.: Positive observers and dynamic output-feedback controllers for interval positive linear systems. IEEE Trans. Circuits Syst. I: Regul. Pap. 55, 3209–3222 (2008)

    Article  MathSciNet  Google Scholar 

  16. Tanaka, K., Ikedea, T., Wang, H.O.: Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, control theory, and linear matrix inequalities. IEEE Trans. Fuzzy Syst. 4(1), 1–13 (1996)

    Article  Google Scholar 

  17. Yang, B., Lin, W.: Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization. IEEE Trans. Autom. Control 50(5), 619–630 (2005)

    Article  MathSciNet  Google Scholar 

  18. Zaidi I., Tadeo F., Chaabane M.: Positive observers for continuous time interval positive systems with time-delay. In: 14th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), pp. 225–230 (2013)

    Google Scholar 

  19. Zaidi, I., Chaabane, M., Tadeo, F.: Static state-feedback controller and observer design for interval positive systems with time delay. IEEE Trans. Circuits Syst. II: Expr Briefs 62, 506–510 (2015)

    Article  Google Scholar 

  20. Zhu, X.D., Sun, Y.X.: Observer-based robust stabilization of uncertain dynamic time-delay systems. Control Theory Appl. 13(2), 254–258 (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. College of Mathematics, Physics, and Information Engineering, Zhejiang Normal University, Jinhua, 321004, China

    Yujie Zhao, Linling Liao & Xiushan Cai

  2. School of Electrical Engineering, Zhengzhou University, Zhengzhou, 450001, China

    Yanhong Liu

Authors
  1. Yujie Zhao
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  2. Linling Liao
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  3. Xiushan Cai
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  4. Yanhong Liu
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Corresponding author

Correspondence to Xiushan Cai .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Hong Kong, Hong Kong, Hong Kong

    James Lam

  2. Hangzhou Dianzi University, Hangzhou, China

    Yun Chen

  3. Southwest Minzu University, Chengdu, China

    Xingwen Liu

  4. Dalian University of Technology, Dalian, China

    Xudong Zhao

  5. Hangzhou Dianzi University, Hangzhou, China

    Junfeng Zhang

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Zhao, Y., Liao, L., Cai, X., Liu, Y. (2019). Stabilization Design for Uncertain Linear Positive Systems with Time-Delay. In: Lam, J., Chen, Y., Liu, X., Zhao, X., Zhang, J. (eds) Positive Systems . POSTA 2018. Lecture Notes in Control and Information Sciences, vol 480. Springer, Cham. https://doi.org/10.1007/978-3-030-04327-8_13

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