C. Marin and E.D. Marin (Romania)
Identification, Distribution theory, Moments, Functionals.
The paper presents new aspects of the system identifica tion based on distribution theory presented for the first time in [1], [2], called DBI (Distribution Based Identifi cation). The finite order fundamental spaces properties are considered. The problem of continuous time system identification versus discrete time is analysed. First, the identification problem of a linear proper sys tem is formulated in function spaces based on derivative operators. The identificability is presented as a condition to vanish a continuous time function. All these aspects are formulated in the distribution framework. The equiva lence between identificability condition in function spaces and that defined in distribution spaces is pre sented. In the proposed approach of identification, the derivatives are present in background but only their im ages as distributions are utilised in practice. Some appli cations of the continuous system identification based on distributions are presented. The problem of testing func tions generation under a unitary set of programs is ana lysed. Four types of fundamental functions, each of them in three variants are implemented. Through some exam ples, the potential of the method is revealed.
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