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Exponential stabilisation and dissipativity analysis of semilinear parabolic systems

Author

Listed:
  • K. Mathiyalagan
  • R. Ragul
  • Ju H. Park
  • J. Palraj

Abstract

In this paper, exponential stabilisation and dissipativity analysis for the scalar distributed parameter system governed by semilinear partial differential equations (PDE) are investigated. The PDE under consideration is the parabolic type with unstable dynamics and assumed to have an external disturbance and mixed boundary conditions. First, the existence and uniqueness results for the PDE are discussed using semigroup theory. Then the sufficient conditions to guarantee the exponential stability and dissipativity are obtained using the Lyapunov stability theory. Finally, the results are verified through numerical examples.

Suggested Citation

  • K. Mathiyalagan & R. Ragul & Ju H. Park & J. Palraj, 2020. "Exponential stabilisation and dissipativity analysis of semilinear parabolic systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(12), pages 2181-2191, September.
    • Handle: RePEc:taf:tsysxx:v:51:y:2020:i:12:p:2181-2191
    DOI: 10.1080/00207721.2020.1793228
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    Cited by:

    1. Nguyen, Ngoc Hoai An & Kim, Sung Hyun, 2021. "Asynchronous dissipative control design for semi-Markovian jump systems with uncertain probability distribution functions of sojourn-time," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    2. Yan, Zhilian & Guo, Tong & Zhao, Anqi & Kong, Qingkai & Zhou, Jianping, 2022. "Reliable exponential H∞ filtering for a class of switched reaction-diffusion neural networks," Applied Mathematics and Computation, Elsevier, vol. 414(C).

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