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Abstract  

We characterize the stabilization for some coupled infinite dimensional systems. The proof of the main result uses the methodology introduced in Ammari and Tucsnak [2], where the exponential stability for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined to a boundedness property of the transfer function of the associated open loop system and a result in [11].

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Abstract  

This paper is a review of recent developments of a research line proposed on the turn of the decades, 1980s to 1990s. The main results concern basic qualitative properties of nonlinear models of population biology, such as controllability and observability. The methods applied are different for the density-dependent models of population ecology and for the frequency-dependent models of population genetics and evolutionary theory. While in the first case the classical theorems of nonlinear systems theory can be used, in the second one an extension of classical results to systems with invariant manifold is necessary.

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