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🆕 Date Issued:
2020-02-25
🗄 In DepositOnce:2023-07-17
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Exponential Stability for the Schlögl System by Pyragas Feedback

Gugat, Martin; Mateos, Mariano; Tröltzsch, Fredi

The Schlögl system is governed by a nonlinear reaction-diffusion partial differential equation with a cubic nonlinearity. In this paper, feedback laws of Pyragas-type are presented that stabilize the system in a periodic state with a given period and given boundary traces. We consider the system both with boundary feedback laws of Pyragas type and distributed feedback laws of Pyragas and classical type. Stabilization to periodic orbits is important for medical applications that concern Parkinson’s disease. The exponential stability of the closed loop system with respect to the L2-norm is proved. Numerical examples are provided.
Lyapunov functionboundary feedbackRobin feedbackparabolic partial differential equationexponential stabilitystabilization of periodic orbitsperiodic operationstabilization of desired orbitsPoincaré–Friedrichs inequalitydelay differential equations49J2093B5293C20
Published in: Vietnam Journal of Mathematics, 10.1007/s10013-020-00382-7, Springer
Creative Commons Attribution 4.0 (CC BY)Creative Commons Attribution 4.0 (CC BY)
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