https://doi.org/10.1140/epjs/s11734-024-01414-w
Regular Article
Backstepping-based boundary control design for reaction-diffusion equations with delays
1
Department of Mathematics, Bharathiar University, 641046, Coimbatore, Tamilnadu, India
2
Department of Mathematics, SRM Institute of Science and Technology, 621105, Tiruchirappalli, Tamilnadu, India
Received:
22
March
2024
Accepted:
14
November
2024
Published online:
2
December
2024
This paper deals with the design of boundary control to stabilize the unstable reaction-diffusion equation with state delay. The backstepping method using the Volterra integral transformation is used for designing the boundary control. Stabilization of the chosen target system is proved using passivity theory which is the main novelty of this paper. By constructing an appropriate Lyapunov function for the target system, the conditions for proving the decreasing nature of Lyapunov function are established in terms of linear matrix inequality. The result ensures the asymptotical stability and passivity of the given system with Neumann boundary conditions without disturbance and with disturbance, respectively. A numerical example is illustrated in detail, which shows the passivity and internal stability of the system.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
