### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 581-585 |

Number of pages | 5 |

Journal | IEEE Transactions on Automatic Control |

Volume | 39 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 1994 |

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### ASJC Scopus subject areas

- Control and Systems Engineering
- Electrical and Electronic Engineering

### Cite this

*IEEE Transactions on Automatic Control*,

*39*(3), 581-585. https://doi.org/10.1109/9.280764

**Delta-operator formulated discrete-time approximations of continuous-time systems.** / Premaratne, Kamal; Salvi, R.; Habib, N. R.; LeGall, J. P.

Research output: Contribution to journal › Article

*IEEE Transactions on Automatic Control*, vol. 39, no. 3, pp. 581-585. https://doi.org/10.1109/9.280764

}

TY - JOUR

T1 - Delta-operator formulated discrete-time approximations of continuous-time systems

AU - Premaratne, Kamal

AU - Salvi, R.

AU - Habib, N. R.

AU - LeGall, J. P.

PY - 1994/3/1

Y1 - 1994/3/1

N2 - 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.

AB - 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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U2 - 10.1109/9.280764

DO - 10.1109/9.280764

M3 - Article

VL - 39

SP - 581

EP - 585

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 3

ER -