Boundary Control of Boundary Coupled Parabolic Distributed Parameter Systems based on Partial State Transformation

Abstract

This paper considers a boundary stabilization problem of systems described by boundary coupled two one-dimensional parabolic partial differential equations based on the backstepping method. Unlike the conventional backstepping framework, we propose a state transformation that contains the state of the unforced subsystem partially. It is proved that this transformation is well-defined and converts the original system into an exponentially stable system together with an associated state feedback control law under a condition that ensures the stability of the unforced subsystem. The original system with this control law inherits the stability of the transfomed one. The effectiveness of the obtained control law is demonstrated numerically.