| In this work, the dynamics of nitrogen absorption, distribution and translocation in citrus trees is modelled to get information we can use to improve the criteria that are followed in the nitrogen fertilization of citrus at present. For that, we use a compartmental N-periodic system of period N = 365 given by an space-state model. After the model is obtained, we study its structural properties and the stability. The aim of the model is to use it to make simulations with different fertilizer programs and hence to fit it. The model can help us to improve the nitrogen fertilization efficiency in citrus.; But, the data we need to construct this type of space-state model are not always available and we have to resort to an input-output model given by the transfer matrix. The transfer matrix explains the input-output relationships in a system and gives a perfect description of the system dynamic characteristics, although it does not give a physic description. The settling of an inner description of the system from the transfer matrix is call realization.; Then, other important subject we deal in this work is the compartmental realization problem. That is to say, given a transfer matrix G(p) to obtain a compartmental triple (C, A, B) such that G(p) = C(pI - A)-1 B. We characterize the transfer function of compartmental systems composed by n single compartments interconnected in serie and/or in parallel, because this kind of systems are usual in the research of nutrients flows in an organism. An example is the nitrogen dynamics model in citrus trees. We study these control systems taking into account the following classification: single-input single-output systems (SISO), first is continuous time and then in discrete time, multi-input multi-output systems (MIMO) and N-periodic systems. We prove that these transfer matrices admit a typical compartmental realization, that we have called basic bidiagonal realization. Afterwards, we relate the basic bidiagonal realization with some canonical forms present in the literature on positive and compartmental SISO systems. Moreover, we will obtain that the basic bidiagonal realization can be considered not only for an asymptotically stable transfer matrix, but also for simply stable one. |
