External Positivity of Discrete-Time Linear Systems: Transfer Function Conditions and Output Feedback

• 成果类型: Article
• 署名作者: Taghavian, Hamed; Johansson, Mikael
• 署名单位: Royal Institute of Technology; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3247546
• 发表日期: 2023
• 页码: 6649-6663
• 关键词: External positivity; positive systems; Bell polynomials; overshooting; Convex Optimization; optimal control; output-feedback.

摘要

This article develops an optimization-based synthesis procedure for fixed-order output-feedback controllers, ensuring a stable closed-loop system with a monotonic step response and rejection of persistent disturbances. This result is based on a unified set of external positivity conditions for discrete-time linear systems. The conditions are derived using an alternative technique for the inverse Z-transform of rational transfer functions based on Bell polynomials and a convenient recurrence relation for the impulse response. Our approach yields a necessary and sufficient condition expressed as polynomial inequalities in the transfer function coefficients. Under additional assumptions, we derive a sequence of weaker but numerically more tractable conditions, leading to an efficient controller synthesis procedure.