BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL.
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| Titel: | BOUNDARY STABILIZATION OF A CLASS OF COUPLED REACTION-DIFFUSION SYSTEM WITH ONE CONTROL. |
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| Autoren: | ARIAS, GONZALO1 ngonzaloandres@uc.cl, PARADA, HUGO2 hugo.parada@math.univ-toulouse.fr |
| Quelle: | SIAM Journal on Control & Optimization. 2025, Vol. 63 Issue 4, p2783-2808. 26p. |
| Schlagwörter: | *CONTROL theory (Engineering), BACKSTEPPING control method, SINGULAR perturbations, DIFFUSION coefficients, STABILITY theory, REACTION-diffusion equations, EIGENVALUES |
| Abstract: | Controllability and stabilization of coupled reaction-diffusion systems has been widely studied in the last few decades. In recent years, coupling reaction-diffusion systems to elliptic equations has been gaining attention. These systems arise as a simplified model for coupled reactiondiffusion systems when at least one diffusion coefficient is high. In this article, we study the eigenvalues of a coupled reaction-diffusion system with one high diffusion. As a consequence, when this system is unstable we are able to build a Backstepping-based controller to stabilize it. This is achieved due to the singular perturbation method (SPM), which provides a methodology to study the behavior of the eigenvalues with respect to the singular perturbation parameter. Additionally, the SPM helps in building controller based on the reduced models, which are used to stabilize the coupled system when one diffusion is high enough. [ABSTRACT FROM AUTHOR] |
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| Datenbank: | Business Source Index |
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