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Delta-operator formulated discrete-time approximations of continuous-time systems

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4 Author(s)
Premaratne, K. ; Dept. of Electr. & Comput. Eng., Miami Univ., Coral Gables, FL, USA ; Salvi, R. ; Habib, N.R. ; LeGall, J.P.

Given a continuous-time system, a technique to directly obtain an approximate delta-operator formulated discrete-time system (δ-system) is presented. For this purpose, the analog of the well known Boxer-Thaler integrators (q-forms) applicable to shift-operator formulated discrete-time systems (q-systems) are derived for δ-systems. Next, using these δ-forms, a method to obtain an approximate δ-system of a given continuous-time system is derived. This algorithm is easily implementable in a computer with little computational burden. It is shown that, as sampling time decreases, the δ-system thus obtained yields the given continuous-time system further verifying the close equivalence between this formulation and continuous-time systems. Two examples illustrating advantages that may be gained by utilizing these δ-forms in digitizing analog systems are also included

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Automatic Control, IEEE Transactions on  (Volume:39 ,  Issue: 3 )