Boundary control for a partial differential equation-ordinary differential equation system cascaded at internal point
GUO Chun-li
ZHOU Zhong-cheng
Abstract：Stabilization of a partial differential equation-ordinary differential equation (PDE-ODE) system cascaded at internal point is considered by boundary control. This system is more complicated than the conventional ones because the interconnection point is the internal point x0 ∈ (0, 1). For this new system, a new backstepping transformation is introduced, which contains four kernel functions. Because the number of kernels is increased, the kernel equations with the compatibility conditions are more complicated. Fortunately, the kernel equations can be solved by a series of mathematical tricks to obtain their solutions. Then, the feedback controller is developed by using these kernel functions. The inverse transformation is derived by using the same procedure. Finally, we choose a proper norm and establish the stability of the closed-loop system by the boundedness of the transformation and the inverse transformation.
Keywords：PDE-ODE cascaded systemboundary controlstabilitybackstepping method
Publication Date：2014-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：7( 779-785 )