Implementation of fractional-order difference via Takenaka-Malmquist functions

作者：

Highlights：

• A new definition of fractional-order difference based on the Takenaka-Malmquist filters has been introduced.

• The finite-length implementations of the Takenaka-Malmquist-based difference and discrete-time integrator are proposed.

• The Takenaka-Malmquist-based difference is applied in modeling the discrete-time non-commensurate fractional-order state-space system.

• The proposed methodology is highly effective in modeling fractional-order difference, integrator, and fractional-order state-space system.

摘要

•A new definition of fractional-order difference based on the Takenaka-Malmquist filters has been introduced.•The finite-length implementations of the Takenaka-Malmquist-based difference and discrete-time integrator are proposed.•The Takenaka-Malmquist-based difference is applied in modeling the discrete-time non-commensurate fractional-order state-space system.•The proposed methodology is highly effective in modeling fractional-order difference, integrator, and fractional-order state-space system.

论文关键词：Nabla discrete-time difference,Grünwald-Letnikov difference,Takenaka-Malmquist functions,Non-commensurate fractional-order state-space system

论文评审过程：Received 14 February 2022, Revised 13 May 2022, Accepted 27 July 2022, Available online 7 August 2022, Version of Record 18 August 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127452