Exponential stabilisation and dissipativity analysis of semilinear parabolic systems

K. Mathiyalagan, R. Ragul, Ju H. Park and J. Palraj

International Journal of Systems Science, 2020, vol. 51, issue 12, 2181-2191

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.

Date: 2020
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DOI: 10.1080/00207721.2020.1793228

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