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Non-Minimality of the realizations and possessing state matrices with integer elements in linear discrete-time controllers

Tavazoei, M. S ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1109/TAC.2022.3192811
  3. Publisher: Institute of Electrical and Electronics Engineers Inc , 2022
  4. Abstract:
  5. 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 introduced framework, a class of unstable controllers is introduced which can be realized by state-space forms having state matrices with integer elements. Numerical examples are presented to verify the usefulness of the introduced framework in the realization of unstable controllers with integer state matrices. IEEE
  6. Keywords:
  7. Control systems ; Discrete-time controller ; Encrypted control systems ; Finite impulse response filters ; Integer state matrix ; Matrices ; pisot numbers ; State-space methods ; Controllers ; Cryptography ; Discrete time control systems ; Eigenvalues and eigenfunctions ; Impulse response ; Linear systems ; Matrix algebra ; Algebraic integers ; Discrete-time controllers ; Eigenvalue and eigenfunctions ; Encrypted control system ; Matrix ; Minimality ; State matrix ; State-space method ; State space methods
  8. Source: IEEE Transactions on Automatic Control ; 2022 , Pages 1-6 ; 00189286 (ISSN)
  9. URL: https://ieeexplore.ieee.org/document/9835020