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

Document Type

Article

Publication Date

2-1-2023

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.

Publication Source (Journal or Book title)

IEEE Transactions on Circuits and Systems I: Regular Papers

First Page

819

Last Page

832

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