We consider systems of $ n $ parabolic equations coupled in zero or first order terms with $ m $ scalar controls acting through a control matrix $ B $. We are interested in stabilization with a control in feedback form. Our approach relies on the approximate controllability of the linearized system, which in turn is related to unique continuation property for the adjoint system. For the unique continuation we establish algebraic Kalman type conditions.

中文翻译：

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零或一阶耦合的抛物线系统的内部反馈稳定

我们考虑抛物线方程组n的抛物线方程组在零阶或一阶条件下与通过控制矩阵$ B $作用的$ m $标量控制耦合。我们对通过反馈形式进行控制的稳定性感兴趣。我们的方法依赖于线性化系统的近似可控性，而线性化系统又与伴随系统的唯一连续性有关。对于唯一的延续，我们建立了代数卡尔曼型条件。