The Direct Feedback Control and Exponential Stabilization of a Coupled Heat PDE-ODE System with Dirichlet Boundary Interconnection

摘要

This paper addresses the exponential stability for an interconnected system of an nth-order ODE system with the input governed by the Dirichlet boundary of a heat equation, and conversely, the output of the ODE is fluxed into the heat equation. The semigroup approach is adopted to show that the system operator is well-posed. We establish the exponential stability of the system by Riesz basis method. Furthermore, with MATLAB software, some numerical simulations are presented to show the effectiveness of the interconnection between the heat PDE and ODE systems.