On the uniform input-to-state stability of reaction-diffusion systems

Abstract— In the present paper we consider uniform inputto-state stability of reaction-diffusion equations and compare it with its finite dimensional counterpart without diffusion as a parameterized set of decoupled equations. The reactiondiffusion partial differential equation can be seen as their interconnection via diffusion. We prove, that for linear reactiondiffusion systems and certain classes of nonlinear equations the UISS property for corresponding systems without diffusion implies, that the UISS property holds also for the system with diffusion.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Sergey Dashkovskiy, Andrii Mironchenko
• Keywords: CDC 2010, Control Systems, Dimensional Counterpart, Nonlinear Equations, Reaction Diffusion Equations