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This chapter treats the result of null controllability of a coupled parabolic system with dynamic boundary conditions containing a coupling matrix A and control matrix B that are constants, and \(A_\Gamma \) is an additional coupling matrix on the boundary. We will prove that the Kalman rank condition \(rank[A|B]=n\) is a sufficient condition for the null controllability of the system. However, we will emphasize that the Kalman rank condition is only a necessary condition under a stability assumption on the matrix \(A_\Gamma \) . Our approach involves establishing Carleman and observability inequalities for the corresponding adjoint problem.

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Kalman Condition for Null Controllability for Parabolic Systems with Dynamic Boundary Conditions

  • 会议论文

  • 发表日期：

    2026年

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  • Mariem Jakhoukh,
  • Lahcen Maniar

摘要

This chapter treats the result of null controllability of a coupled parabolic system with dynamic boundary conditions containing a coupling matrix A and control matrix B that are constants, and \(A_\Gamma \) is an additional coupling matrix on the boundary. We will prove that the Kalman rank condition \(rank[A|B]=n\) is a sufficient condition for the null controllability of the system. However, we will emphasize that the Kalman rank condition is only a necessary condition under a stability assumption on the matrix \(A_\Gamma \) . Our approach involves establishing Carleman and observability inequalities for the corresponding adjoint problem.