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Hyperbolic observer design for a class of nonlinear systems

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  • Parvizian, Majid
  • Khandani, Khosro

Abstract

In this paper the problem of hyperbolic observer design for a class of nonlinear systems is addressed for the first time. The asymptotic stability of the estimation error dynamics is proven by employing the Lyapunov stability analysis method and using Taylor series for hyperbolic functions, and then the sufficient conditions are derived in the form of Linear Matrix Inequalities (LMIs). Also a hyperbolic non-fragile adaptive observer is introduced for a class of uncertain nonlinear systems with time delay. It is shown that the proposed observer performs effectively in dealing with large estimation errors. Three illustrative examples of Chen, Rössler and a financial system are provided which corroborate the effectiveness of the propose method.

Suggested Citation

  • Parvizian, Majid & Khandani, Khosro, 2021. "Hyperbolic observer design for a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001375
    DOI: 10.1016/j.chaos.2021.110785
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    References listed on IDEAS

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    1. Sharma, Vivek & Shukla, Manoj & Sharma, B.B., 2018. "Unknown input observer design for a class of fractional order nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 96-107.
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    3. Fu, Shihui & Liu, Yuan & Ma, Huizhen & Du, Ying, 2020. "Control chaos to different stable states for a piecewise linear circuit system by a simple linear control," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Alamdar Hafezi & Khosro Khandani & Vahid Johari Majd, 2020. "Non-fragile exponential polynomial observer design for a class of nonlinear fractional-order systems with application in chaotic communication and synchronisation," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(8), pages 1353-1372, June.
    5. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
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