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

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  • Manna Li
  • Weijie Mao

Abstract

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.

Suggested Citation

  • Manna Li & Weijie Mao, 2020. "Finite-Time Bounded Control for Coupled Parabolic PDE-ODE Systems Subject to Boundary Disturbances," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, December.
    • Handle: RePEc:hin:jnlmpe:8882382
    DOI: 10.1155/2020/8882382
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