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Non-Minimality of the realizations and possessing state matrices with integer elements in linear discrete-time controllers
, Article IEEE Transactions on Automatic Control ; 2022 , Pages 1-6 ; 00189286 (ISSN) ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2022
Abstract
It is known that discrete-time controllers, whose state matrices have no non-integer element, are beneficial in homomorphic based encrypted control systems. Nevertheless, it has been recently shown that possessing state matrices with integer elements usually yields unstable discrete-time controllers. In this note, we investigate the problem from a non-minimality perspective. It is shown that non-minimal realizations, in comparison to minimal ones, can theoretically provide a wider framework to obtain controllers having state matrices with integer elements. However, in the case of dealing with BIBO stable controllers, this framework cannot preserve internal stability. But, benefiting from the...