Abstract
The classical Leslie model used for describing the natural growth of age-structured populations is adapted to the case of controlled populations. Such a model is a nonlinear positive system with non-negative inputs and enjoyes remarkable structural properties. The non-trivial equilibria are critically stable but can be stabilized by a state variable feedback. The set of states reachable from any given initial state is a positive cone generated by n reachability vectors b, Ab,…, A n−1b . The system is completely observable and its state can be reconstructed provided the input sequence can be suitably programmed. All these properties constitute an important theoretical framework for population control problems.
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