A Maximum Principle-based Approach for Input-to-State Stability Analysis of Parabolic Equations with Boundary Disturbances

Abstract

This paper introduces a maximum principle-based approach for the establishment of input-to-state stability (ISS) for parabolic equations with different type of boundary disturbances. A classical result on the estimate of the solutions to linear parabolic partial differential equations (PDEs) has been extended, which enables the application of the maximum principle to ISS analysis of certain linear or nonlinear parabolic PDEs. The effectiveness of this approach is demonstrated through the establishment of the ISS properties of a nonlinear parabolic equation with Dirichlet boundary disturbances in higher dimensional space, a 1-D linear parabolic equation with mixed boundary disturbances, and the Chafee-Infante equation with Robin boundary disturbances.