Nonminimality of the Realizations and Possessing State Matrices With Integer Elements in Linear Discrete-Time Controllers

• 成果类型: Article
• 署名作者: Tavazoei, Mohammad Saleh
• 署名单位: Sharif University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3192811
• 发表日期: 2023
• 页码: 3698-3703
• 关键词: Matrices; Eigenvalues and eigenfunctions; Linear systems; control systems; cryptography; State-space methods; Finite impulse response filters; Algebraic integers; discrete-time controller; encrypted control systems; integer state matrix; pisot numbers

摘要

It is known that discrete-time controllers, whose state matrices have no noninteger 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 article, we investigate the problem from a nonminimality perspective. It is shown that nonminimal 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 bounded-input bounded-output (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.