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Sliding-mode observer design and finite-time control of one-sided Lipschitz nonlinear systems with time-delay

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Abstract

This paper is concerned with finite-time observer-based control of time-delay systems with one-sided Lipschitz nonlinearity and unknown energy-bounded exogenous disturbances. For this purpose, first, a robust sliding-mode observer is designed and the dynamical equations of the observer error are obtained. Then, the observer-based controller is designed to yield the finite-time boundedness of the time-delay closed-loop system and also satisfies the passivity performance index. By selecting the appropriate Lyapunov–Krasovskii functional, which is function of both systems states and observer error, the sufficient conditions are derived for robust finite-time boundedness of the closed-loop nonlinear one-sided Lipschitz system. In this regard, two theorems are given and the sufficient conditions are derived in terms of feasibility testing of the extracted linear matrix inequalities. Finally, computer simulations are performed to verify the theoretical achievements.

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References

  • Abbaszadeh M, Marquez HJ (2010) Nonlinear observer design for one-sided Lipschitz systems. In: American control conference (ACC), 2010. IEEE, pp 5284–5289

  • Abid H, Toumi A (2016) Adaptive fuzzy sliding mode controller for a class of SISO nonlinear time-delay systems. Soft Comput 20(2):649–659

    Article  MATH  Google Scholar 

  • Ali MS, Saravanan S (2016) Robust finite-time \(H\infty \) control for a class of uncertain switched neural networks of neutral-type with distributed time varying delays. Neurocomputing 177:454–468

    Article  Google Scholar 

  • Ali MS, Saravanan S, Cao J (2017) Finite-time boundedness, L2-gain analysis and control of Markovian jump switched neural networks with additive time-varying delays. Nonlinear Anal Hybrid Syst 23:27–43

    Article  MathSciNet  MATH  Google Scholar 

  • Amato F, Ariola M (2005) Finite-time control of discrete-time linear systems. IEEE Trans Autom Control 50(5):724–729

    Article  MathSciNet  MATH  Google Scholar 

  • Benallouch M, Boutayeb M, Zasadzinski M (2012) Observer design for one-sided Lipschitz discrete-time systems. Syst Control Lett 61(9):879–886

    Article  MathSciNet  MATH  Google Scholar 

  • Binazadeh T (2016) Finite-time tracker design for uncertain nonlinear fractional-order systems. J Comput Nonlinear Dyn 11(4):041028

    Article  MathSciNet  Google Scholar 

  • Binazadeh T, Yousefi M (2017) Designing a cascade-control structure using fractional-order controllers: time-delay fractional-order proportional–derivative controller and fractional-order sliding-mode controller. J Eng Mech 143(7):04017037

    Article  Google Scholar 

  • Chen C, Feng G, Guan X (2005) An adaptive lag-synchronization method for time-delay chaotic systems. In: American control conference, 2005. Proceedings of the 2005. IEEE, pp 4277–4282

  • Dong Y, Liu W, Li T, Liang S (2017) Finite-time boundedness analysis and H\(_{\infty }\) control for switched neutral systems with mixed time-varying delays. J Franklin Inst 354(2):787–811

    Article  MathSciNet  MATH  Google Scholar 

  • Ghaemi S, Sabahi K, Badamchizadeh MA (2018) Lyapunov–Krasovskii stable T2FNN controller for a class of nonlinear time-delay systems. Soft Comput. https://doi.org/10.1007/s00500-018-3053-9

  • Gholami H, Binazadeh T (2018) Design finite-time output feedback controller for nonlinear discrete-time systems with time-delay and exogenous disturbances. Syst Sci Control Eng 6(1):20–27

    Article  Google Scholar 

  • Jiao T, Zong G, Zheng W (2013) New stability conditions for GRNs with neutral delay. Soft Comput 17(4):703–712

    Article  MATH  Google Scholar 

  • Khalil HK (2014) Nonlinear control. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Li Z, Fei Z, Karimi HR (2016) New results on stability analysis and stabilization of time-delay continuous Markovian jump systems with partially known rates matrix. Int J Robust Nonlinear Control 26(9):1873–1887

    Article  MathSciNet  MATH  Google Scholar 

  • Liu H, Shi P, Karimi HR, Chadli M (2016) Finite-time stability and stabilisation for a class of nonlinear systems with time-varying delay. Int J Syst Sci 47(6):1433–1444

    Article  MathSciNet  MATH  Google Scholar 

  • Mohammadpour S, Binazadeh T (2018) Observer-based synchronization of uncertain chaotic systems subject to input saturation. Trans Inst Meas Control 40(8):2526–2535

    Article  Google Scholar 

  • Moulay E, Dambrine M, Yeganefar N, Perruquetti W (2008) Finite-time stability and stabilization of time-delay systems. Syst Control Lett 57(7):561–566

    Article  MathSciNet  MATH  Google Scholar 

  • Nguyen MC, Trinh H (2016a) Reduced-order observer design for one-sided Lipschitz time-delay systems subject to unknown inputs. IET Control Theory Appl 10(10):1097–1105

    Article  MathSciNet  Google Scholar 

  • Nguyen MC, Trinh H (2016b) Unknown input observer design for one-sided Lipschitz discrete-time systems subject to time-delay. Appl Math Comput 286:57–71

    MathSciNet  MATH  Google Scholar 

  • Pazhooh F, Shahraki F, Sadeghi J, Fakhroleslam M (2018) Multivariable adaptive neural network predictive control in the presence of measurement time-delay: application in control of Vinyl Acetate monomer process. J Process Control 66:39–50

    Article  Google Scholar 

  • Rahimi N, Binazadeh T (2018) Distributed robust consensus control for nonlinear leader–follower multi-agent systems based on adaptive observer-based sliding mode. J Vib Control 24:1077546318772239

    Google Scholar 

  • Rajavel S, Samidurai R, Cao J, Alsaedi A, Ahmad B (2017) Finite-time non-fragile passivity control for neural networks with time-varying delay. Appl Math Comput 297:145–158

    MathSciNet  MATH  Google Scholar 

  • Sabahi K, Ghaemi S, Badamchizadeh M (2016) Designing an adaptive type-2 fuzzy logic system load frequency control for a nonlinear time-delay power system. Appl Soft Comput 43:97–106

    Article  Google Scholar 

  • Sanz R, Garcia P, Zhong Q-C, Albertos P (2017) Predictor-based control of a class of time-delay systems and its application to quadrotors. IEEE Trans Ind Electron 64(1):459–469

    Article  Google Scholar 

  • Saravanakumar R, Ali MS, Hua M (2016) H\(_{\infty }\) state estimation of stochastic neural networks with mixed time-varying delays. Soft Comput 20(9):3475–3487

    Article  MATH  Google Scholar 

  • Shi Y, Tang Y, Li S (2017) Finite-time control for discrete time-varying systems with randomly occurring non-linearity and missing measurements. IET Control Theory Appl 11(6):838–845

    Article  MathSciNet  Google Scholar 

  • Song J, He S (2015a) Finite-time \(H\infty \) control for quasi-one-sided Lipschitz nonlinear systems. Neurocomputing 149:1433–1439

    Article  Google Scholar 

  • Song J, He S (2015b) Robust finite-time \(H\infty \) control for one-sided Lipschitz nonlinear systems via state feedback and output feedback. J Frankl Inst 352(8):3250–3266

    Article  MathSciNet  MATH  Google Scholar 

  • Song R, Xiao W, Wei Q, Sun C (2014) Neural-network-based approach to finite-time optimal control for a class of unknown nonlinear systems. Soft Comput 18(8):1645–1653

    Article  MATH  Google Scholar 

  • Song J, Niu Y, Zou Y (2017) Finite-time stabilization via sliding mode control. IEEE Trans Autom Control 62(3):1478–1483

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Shiraz University of Technology, Modares Boulevard, P.O. Box 71555-313, Shiraz, Iran

    Hadi Gholami & Tahereh Binazadeh

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  1. Hadi Gholami
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  2. Tahereh Binazadeh
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Correspondence to Tahereh Binazadeh.

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Communicated by V. Loia.

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Gholami, H., Binazadeh, T. Sliding-mode observer design and finite-time control of one-sided Lipschitz nonlinear systems with time-delay. Soft Comput 23, 6429–6440 (2019). https://doi.org/10.1007/s00500-018-3297-4

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