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Observer-based robust exponential stabilization for linear systems with parameter uncertainties

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Abstract

This paper is concerned with the robust observer-based control problem for a class of continuous-time linear systems with parameter uncertainties. A less conservative approach is provided to deal with the quadratic terms involving in the Lyapunov stability analysis for the estimation error dynamic system. Sufficient conditions that ensure the exponential stability of the closed-loop system are established and formulated in terms of linear matrix inequalities. The obtained results are less conservative than some existing ones in recent literature. Finally, two numerical examples are given to show the validity and superiority of the proposed observer-based robust controller.

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References

  1. Wu R, Zhang W, Song F, Wu Z, Guo W (2015) Observer-based stabilization of one-sided Lipschitz systems with application to flexile link manipulator. Adv Mech Eng 7(12):1–8

    Article  Google Scholar 

  2. Zhong F, Li H, Zhong S (2016) State estimation based on fractional order sliding mode observer method for a class of uncertain fractional-order nonlinear systems. Sig Process 127:168–184

    Article  Google Scholar 

  3. Santosh KC (2017) LMI based robust state feedback control of negative-imaginary systems. Int J Dyn Control 5(2):347–356

    Article  MathSciNet  Google Scholar 

  4. Angećlico BA, Barbosa FS, Toriumi FY (2017) State feedback decoupling control of a control moment gyroscope. J Control Autom Electr Syst 28(1):26–35

    Article  Google Scholar 

  5. Tadepalli SK, Leite VJ (2018) Robust stabilization of uncertain 2-D discrete delayed systems. J Control Autom Electr Syst 29(3):280–291

    Article  Google Scholar 

  6. Saravanakumar R, Syed Ali M, Huang H, Cao J, Joo YH (2018) Robust \(H_\infty \) state-feedback control for nonlinear uncertain systems with mixed time-varying delays. Int J Control Autom Syst 16(1):225–233

    Article  Google Scholar 

  7. Zhao Z, Yang Y, Ding SX, Li L (2018) Robust fault detection for observer-based feedback control systems. Circuits Syst Signal Process 37(8):3364–3382

    Article  MathSciNet  Google Scholar 

  8. Khalil HK (2017) Cascade high-gain observers in output feedback control. Automatica 80:110–118

    Article  MathSciNet  Google Scholar 

  9. Zhang W, Su H, Zhu F, Wang M (2013) Observer-based \(H_\infty \) synchronization and unknown input recovery for a class of digital nonlinear systems. Circuits Syst Signal Process 32(6):2867–2881

    Article  MathSciNet  Google Scholar 

  10. Sun L, Zheng Z (2018) Disturbance observer-based robust saturated control for spacecraft proximity maneuvers. IEEE Trans Control Syst Technol 26(2):684–692

    Article  MathSciNet  Google Scholar 

  11. Arcak M, Kokotović P (2001) Observer-based control of systems with slope-restricted nonlinearities. IEEE Trans Autom Control 46(7):1146–1150

    Article  MathSciNet  Google Scholar 

  12. Ekramian M (2017) Observer-based controller for Lipschitz nonlinear systems. Int J Syst Sci 48(16):3411–3418

    Article  MathSciNet  Google Scholar 

  13. Zemouche A, Boutayeb M (2013) On LMI conditions to design observers for Lipschitz nonlinear systems. Automatica 49(2):585–591

    Article  MathSciNet  Google Scholar 

  14. Zhang W, Su H, Zhu F, Bhattacharyya SP (2016) Improved exponential observer design for one-sided Lipschitz nonlinear systems. Int J Robust Nonlinear Control 26(18):3958–3973

    Article  MathSciNet  Google Scholar 

  15. Zhang W, Su H, Zhu F, Azar GM (2015) Unknown input observer design for one-sided Lipschitz nonlinear systems. Nonlinear Dyn 79(2):1469–1479

    Article  MathSciNet  Google Scholar 

  16. Açıkmeşe B, Corless M (2011) Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica 47(7):1339–1348

    Article  MathSciNet  Google Scholar 

  17. Zhao Y, Zhang W, Su H, Yang J (2019) Observer-based synchronization of chaotic systems satisfying incremental quadratic constraints and its application in secure communication. IEEE Trans Syst Man Cybern Syst (to be published). https://doi.org/10.1109/TSMC.2018.2868482

  18. Sadelli L, Fruchard M, Ferreira A (2017) 2D observer-based control of a vascular microrobot. IEEE Trans Autom Control 62(5):2194–2206

    Article  MathSciNet  Google Scholar 

  19. Mokhtari MR, Cherki B, Braham AC (2017) Disturbance observer based hierarchical control of coaxial-rotor UAV. ISA Trans 67:466–475

    Article  Google Scholar 

  20. Zheng F, Zhen Z, Gong H (2017) Observer-based backstepping longitudinal control for carrier-based UAV with actuator faults. J Syst Eng Electron 28(2):322–337

    Article  Google Scholar 

  21. Boulkroune B, Aalst S, Lehaen K, Smet JD (2017) Observer-based controller with integral action for longitudinal vehicle speed control. In: IEEE intelligent vehicles symposium, pp 322–327

  22. Latrach C, Kchaou M, Herveć G (2017) \(H_\infty \) observer-based decentralised fuzzy control design for nonlinear interconnected systems: an application to vehicle dynamics. Int J Syst Sci 48(7):1485–1495

    Article  MathSciNet  Google Scholar 

  23. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Fluids Eng 82(1):35–45

    MathSciNet  Google Scholar 

  24. Luenberger D (1971) An introduction to observers. IEEE Trans Autom Control 16(6):596–602

    Article  Google Scholar 

  25. Lu CY, Tsai JSH, Jong GJ, Su TJ (2003) An LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Trans Autom Control 48(2):286–289

    Article  MathSciNet  Google Scholar 

  26. Gao H, Wang C, Zhao L (2003) Comments on: an LMI-based approach for robust stabilization of uncertain stochastic systems with time-varying delays. IEEE Trans Autom Control 48(11):2073–2074

    Article  Google Scholar 

  27. Lin Z, Guan X, Liu Y, Shi P (2001) Observer-based robust control for uncertain systems with time-varying delay. IMA J Math Control Inf 18(3):439–450

    Article  MathSciNet  Google Scholar 

  28. Heemels W, Daafouz J, Millerioux G (2010) Observer-based control of discrete-time LPV systems with uncertain parameters. IEEE Trans Autom Control 55(9):2130–2135

    Article  MathSciNet  Google Scholar 

  29. Ibrir S, Diopt S (2008) Novel LMI conditions for observer-based stabilization of Lipschitzian nonlinear systems and uncertain linear systems in discrete-time. Appl Math Comput 206(2):579–588

    MathSciNet  MATH  Google Scholar 

  30. Lien C (2004) Robust observer-based control of systems with state perturbations via LMI approach. IEEE Trans Autom Control 49(8):1365–1370

    Article  MathSciNet  Google Scholar 

  31. Kheloufi H, Zemouche A, Bedouhene F, Boutayeb M (2013) On LMI conditions to design observer-based controllers for linear systems with parameter uncertainties. Automatica 49(12):3700–3704

    Article  MathSciNet  Google Scholar 

  32. Boyd S, Ghaoui L, Feron E, Balakrishan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia

    Book  Google Scholar 

  33. Wang S, Jiang Y (2014) Comment on: on LMI conditions to design observer-based controllers for linear systems with parameter uncertainties. Automatica 50(10):2732–2733

    Article  MathSciNet  Google Scholar 

  34. Lens H (2009) Fast robust stabilization by saturating output feedback of uncertain linear systems with input constraints. In: 2009 IEEE Conference on Decision and Control, pp 6935–6940

  35. Ostertag E (2008) An improved path-following method for mixed \(H_2\) /\(H_\infty \) controler design. IEEE Trans Autom Control 53(8):1967–1971

    Article  MathSciNet  Google Scholar 

  36. Li X, Lu D, Zeng G, Liu J, Zhang W (2017) Integrated fault estimation and non-fragile fault-tolerant control design for uncertain Takagi-Sugeno fuzzy systems with actuator fault and sensor fault. IET Control Theory Appl 11(10):1542–1553

    Article  MathSciNet  Google Scholar 

  37. De Souza CE, Li X (1999) Delay-dependent robust control of uncertain linear state-delayed systems. Automatica 35(7):1313–1321

    Article  MathSciNet  Google Scholar 

  38. Chang X, Yang G (2014) New results on output feedback \(H_\infty \) control for linear discrete-time systems. IEEE Trans Autom Control 59(5):1355–1359

    Article  MathSciNet  Google Scholar 

  39. Khalil HK (1996) Noninear systems. Prentice-Hall, Upper Saddle River

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mechnical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Xuesheng Zhang, Lin Long & Wei Zhang

  2. School of Information Technology and Mechanical and Electrical Integration, Shanghai Zhongqiao College, Shanghai, 201310, China

    Jian Hu

Authors
  1. Xuesheng Zhang
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  2. Jian Hu
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  3. Lin Long
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  4. Wei Zhang
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Corresponding author

Correspondence to Wei Zhang.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant No. 61603241.

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Zhang, X., Hu, J., Long, L. et al. Observer-based robust exponential stabilization for linear systems with parameter uncertainties. Int. J. Dynam. Control 9, 257–265 (2021). https://doi.org/10.1007/s40435-020-00635-w

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  • DOI: https://doi.org/10.1007/s40435-020-00635-w

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