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Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT

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Abstract

This paper is concerned with the problem of guaranteed cost finite-time control of fractionalorder nonlinear positive switched systems (FONPSS) with D-perturbation. Firstly, the proof of the positivity of FONPSS with D-perturbation is given, the definition of guaranteed cost finite-time stability is firstly given in such systems. Then, by constructing linear copositive Lyapunov functions and using the mode-dependent average dwell time (MDADT) approach, a static output feedback controller is constructed, and sufficient conditions are derived to guarantee that the corresponding closed-loop system is guaranteed cost finite-time stable (GCFTS). Such conditions can be easily solved by linear programming. Finally, an example is provided to illustrate the effectiveness of the proposed method.

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References

  1. Ren Y, Sun G, Feng Z, et al., Weighted-average l1 filtering for switched positive systems, Int. J. Robust Nonlin., 2017, 27(18): 5097–5115.

    Article  MATH  Google Scholar 

  2. Sun Y, Tian Y, and Xie X, Stabilization of positive switched linear systems and its application in consensus of multi-agent systems, IEEE T Automat. Contr., 2017, 62(12): 6608–6613.

    Article  MATH  Google Scholar 

  3. Liu J, Zhang K, Pang G, et al., Controller synthesis for constrained discrete-time switched positive linear systems, Nonlinear Anal-Hybri, 2016, 19: 1–12.

    Article  MathSciNet  MATH  Google Scholar 

  4. Hartley T T, Lorenzo C F, and Qammer H K, Chaos in a fractional-order Chua’s system, IEEE T CIRCUITS-I-Regular Papers, 1995, 42(8): 485–490.

    Article  Google Scholar 

  5. Aghababa M P and Borjkhani M, Chaotic fractional-order model for muscular blood vessel and its control via fractional control scheme, Complexity, 2014, 20(2): 37–46.

    Article  MathSciNet  Google Scholar 

  6. Ortigueira M and Machado J, Special issue on fractional signal processing and applications, Signal Process, 2003, 83(11): 2285–2480.

    Article  Google Scholar 

  7. Hilfer R, Application of fractional calculus in physics, World Scientific, 2000, 35(12): 87–130.

    MATH  Google Scholar 

  8. Shen J and Lam J, Stability and performance analysis for positive fractional-order systems with time-varying delays, IEEE T Automat. Contr., 2016, 61(9): 2676–2681.

    Article  MathSciNet  MATH  Google Scholar 

  9. Benzaouia A, Hmamed A, and Mesquine F, Stabilization of continuous-time fractional positive systems by using a lyapunov function, IEEE T Automat. Contr., 2014, 59(8): 2203–2208.

    Article  MathSciNet  MATH  Google Scholar 

  10. Babiarz A, Legowski A, and Niezabitowski M, Controllability of positive discrete-time switched fractional order systems for fixed switching sequence, Lecture Notes in Artificial Intelligence, 2016, 9875: 303–312.

    Google Scholar 

  11. Zhao X, Yin Y, and Zheng X, State-dependent switching control of switched positive fractionalorder systems, ISA Transactions, 2016, 62: 103–108.

    Article  Google Scholar 

  12. Peter D, Short time stability in linear time-varying systems, Proc. IRE Int. Convention Record Part 4, 1961, 83–87.

    Google Scholar 

  13. Xiang M and Xiang Z, Finite-time L1 control for positive switched linear systems with timevarying delay, Commun. Nonlinear Sci., 2013, 18(11): 3158–3166.

    Article  MathSciNet  MATH  Google Scholar 

  14. Liu J, Lian J, and Zhuang Y, Output feedback L1 finite-time control of switched positive delayed systems with MDADT, Nonlinear Anal-Hybri, 2015, 15: 11–22.

    Article  MATH  Google Scholar 

  15. Liu T, Wu B, and Liu L, Asynchronously finite-time control of discrete impulsive switched positive time-delay systems, J Franklin I, 2015, 352(10): 4503–4514.

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhang J, Zhao X, and Chen Y, Finite-time stability and stabilization of fractional order positive switched systems, Circ. Syst. Signal PR, 2016, 35(7): 2450–2470.

    Article  MathSciNet  MATH  Google Scholar 

  17. Liu L, Cao X, Fu Z, et al., Guaranteed cost finite-time control of fractional-order positive switched systems, Advances in Mathematical Physics, 2017, 2017(3): 1–11.

    MathSciNet  Google Scholar 

  18. Wu L and Wang Z, Guaranteed cost control of switched systems with neutral delay via dynamic output feedback, Int. J. Control Autom., 2009, 40(7): 717–728.

    MathSciNet  MATH  Google Scholar 

  19. Behinfaraz R and Badamchizadeh M, Optimal synchronization of two different incommensurate fractional-order chaotic systems with fractional cost function, Complexity, 2016, 21(S1): 401–416.

    Article  MathSciNet  Google Scholar 

  20. Zong G, Wang X, and Zhao H, Robust finite-time guaranteed cost control for impulsive switched systems with time-varying delay, Int. J. Control Autom., 2017, 15(1): 113–121.

    Article  Google Scholar 

  21. Cao X, Liu L, Fu Z, et al., Guaranteed cost finite-time control for positive switched linear systems with time-varying delays, Journal of Control Science and Engineering, 2017, 2017: 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu J, Lian J, and Zhuang Y, Robust stability for switched positive systems with D-perturbation and time-varying delay, Information Sciences, 2016, 369: 522–531.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Leipo Liu, Xiangyang Cao, Zhumu Fu, Shuzhong Song & Hao Xing

Authors
  1. Leipo Liu
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  2. Xiangyang Cao
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  3. Zhumu Fu
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  4. Shuzhong Song
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  5. Hao Xing
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Corresponding author

Correspondence to Leipo Liu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. U1404610, 61473115 and 61374077, Fundamental Research Project under Grant Nos. 142300410293, 142102210564 in the Science and Technology Department of Henan Province, the Science and Technology Research Key Project under Grant No. 14A413001 in the Education Department of Henan Province, and Young Key Teachers Plan of Henan Province under Grant No. 2016GGJS-056.

This paper was recommended for publication by Editor FENG Gang.

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Liu, L., Cao, X., Fu, Z. et al. Guaranteed Cost Finite-Time Control of Fractional-Order Nonlinear Positive Switched Systems with D-Perturbations via MDADT. J Syst Sci Complex 32, 857–874 (2019). https://doi.org/10.1007/s11424-018-7347-x

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  • DOI: https://doi.org/10.1007/s11424-018-7347-x

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