Abstract
The well-posedness of abstract boundary control systems with dynamic boundary conditions (i.e., boundary conditions evolving according to an operator semigroup acting on the boundary space) is established . Here, the boundary feedback operator is unbounded which makes the investigation more interesting in many applications. The positivity of such problem is well studied. By exploiting the positivity, we find a characterization of exponential stability. Our approach is based on the feedback theory of infinite dimensional linear systems. Finally, these results are applied to coupled systems consisting of a partial differential equation (PDE) and an ordinary differential equation (ODE) and to diffusion processes in networks with dynamic ramification nodes.
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