Global feedback stabilizability results are derived for nonautonomous coupled systems arising from the linearization around a given time-dependent trajectory of FitzHugh-CNagumo type systems. The feedback is explicit and is based on suitable oblique (nonorthogonal) projections in Hilbert spaces. The actuators are, typically, a finite number of indicator functions and act only in the parabolic equation. Subsequently, local feedback stabilizability to time-dependent trajectories results are derived for nonlinear coupled parabolic-ODE systems of the FitzHugh-CNagumo type. Simulations are presented showing the stabilizing performance of the feedback control.
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The domain
Norm of solution. Linearization around the steady state
Norm of solution. Linearization around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Linearization around the steady state
Norm of solution. Linearization around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Linearization around the steady state
Norm of solution. Linearization around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Linearization around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Around the time-dependent trajectory
Norm of solution. Linearization around the time-dependent trajectory
PDE only. With