Pisot-Number-Based Discrete-Time Controllers With Integer State Matrices to Ensure Monotonic Closed-Loop Step Responses

• 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.2023.3292177
• 发表日期: 2023
• 页码: 8238-8243
• 关键词: Discrete-time controllers; encrypted control systems; monotonic step response; pisot numbers

摘要

Motivated by the applicability of homomorphically encrypted discrete-time controllers possessing integer state matrices to work in an infinite time horizon, this article deals with the design of such controllers to guarantee that the step response of the control system is monotonic. On the basis of locating the poles of designed controllers at positive Pisot numbers and some of their algebraic conjugates and benefiting from the idea of using nonminimal state-space models, an analytical approach is proposed to obtain discrete-time controllers with integer state matrices, which result in extrema-free closed-loop step responses in control of a class of discrete-time plants whose zeros are between zero and one.