Finite-Time Bounded Control for Coupled Parabolic PDE-ODE Systems Subject to Boundary Disturbances

Abstract EN

In this paper, the finite-time bounded control problem for coupled parabolic PDE-ODE systems subject to time-varying boundary disturbances and to time-invariant boundary disturbances is considered.

First, the concept of finite-time boundedness is extended to coupled parabolic PDE-ODE systems.

A Neumann boundary feedback controller is then designed in terms of the state variables.

By applying the Lyapunov-like functional method, sufficient conditions which ensure the finite-time boundedness of closed-loop systems in the presence of time-varying boundary disturbances and time-invariant boundary disturbances are provided, respectively.

Finally, the issues regarding the finite-time boundedness of coupled parabolic PDE-ODE systems are converted into the feasibility of linear matrix inequalities (LMIs), and the effectiveness of the proposed results is validated with two numerical simulations.