On the Stability of Linear Dynamic Controllers With Integer Coefficients

• 成果类型: Article
• 署名作者: Schluter, Nils; Darup, Moritz Schulze
• 署名单位: Dortmund University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3131126
• 发表日期: 2022
• 页码: 5610-5613
• 关键词: Stability criteria; cryptography; 6G mobile communication; asymptotic stability; Eigenvalues and eigenfunctions; STANDARDS; indexes; Cyclotomic polynomials; encrypted control; integer coefficients; Jury's criterion; linear dynamic control; STABILITY

摘要

In this article, we show that linear dynamic controllers with integer coefficients are usually unstable. In fact, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero. Moreover, for a fixed controller order, there exist only finitely many characteristic polynomials with integer coefficients that lead to marginally stable eigenvalues on the unit circle and we characterize these setups. The obtained results are, in particular, relevant to encrypted control, where (nontrivial) stable controllers with integer coefficients were on the wish list.