Theoretical and Algorithmic Study of Inverses of Arbitrary High-Dimensional Multi-Input Multi-Output Linear-Time-Invariant Systems

Publication Date

2-1-2023

Document Type

Article

Publication Title

IEEE Transactions on Circuits and Systems I: Regular Papers

Volume

70

Issue

2

DOI

10.1109/TCSI.2022.3217980

First Page

819

Last Page

832

Abstract

Nowadays, systems need to be built and/or characterized to handle exceptional circumstances or adapt to a world itself more complex. A typical phenomenon can often be found that systems are required to accommodate high-dimensional inputs and outputs. Although the theories and methods for inverting a single-input single-output (SISO) linear-time-invariant (LTI) system have been well established, the generalized framework (consisting of theories and algorithms) for extending to arbitrary high-dimensional multi-input multi-output (MIMO) scenarios is still unsubstantial in the existing literature as this extension is far from trivial. In this work, we would like to develop such a new framework for governing the inversion of arbitrary high-dimensional discrete-time MIMO LTI systems, where any individual transfer function from a certain input to a certain output may have the infinite-impulse-response (IIR) characteristics. We propose two new inversion algorithms to invert the transfer-function tensors (TFTs) of arbitrary MIMO LTI systems. The pertinent computational complexities are also investigated for our proposed two TFT-inversion algorithms. The approximation of the inverse of an arbitrary TFT by a finite-impulse-response (FIR) TFT is studied and the corresponding approximation-error analysis is derived as well. Finally, numerical evaluations are presented to study the computational complexities with respect to different TFT dimensions and ranks.

Keywords

discrete-time linear time-invariant system, error analysis of approximated inverses, Gaussian elimination procedure, Multiple-input multiple-output (MIMO), transfer-function tensor (TFT)

Department

Applied Data Science

Link to Full Text

Share

COinS