DELTA-OPERATOR FORMULATED DISCRETE-TIME APPROXIMATIONS OF CONTINUOUS-TIME SYSTEMS

Given a continuous-time system, a technique to directly obtain an approximate delta-operator formulated discrete-time system (delta-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 delta-systems. Next, using these delta-forms, a method to obtain an approximate delta-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 delta-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 delta-forms in digitizing analog systems are also included.