One of the general methods in linear control theory is based on harmonic and non-harmonic Fourier series. The key of this approach is the establishment of various suitable adaptations and generalizations of the classical Parseval equality. A new and systematic approach was begun in our papers (1)-(4) in collaboration with Baiocchi. Many recent results of this kind, obtained through various Ingham-type theorems, were exposed recently in (9). Although this work concentrated on continuous models, in connection with numerical simulations a natural question is whether these results also admit useful discrete versions. The purpose of this paper is to establish discrete versions of various Ingham-type theorems by using our approach. They imply the earlier continuous results by a simple limit process.
Applied Mathematics and Optimization – Springer Journals
Published: Mar 1, 2007
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