Exponential input-to-state stability of reaction-diffusion systems

Exponential input-to-state stability (ISS) is an interesting topic and has been paid much attention for the finite-dimensional system. The criterion of exponential ISS for reaction-diffusion systems (RDSs), an infinite dimensional system, is investigated in this paper. Both cases of RDSs with distributed input and boundary input are considered. By employing Lyapunov functional method and inequalities technical, sufficient conditions to guarantee the exponential ISS are obtained. Numerical examples are presented to verify the validity of our results.