Two Classes of Exponentially Stabilizable LPV Systems

• 成果类型: Article
• 署名作者: Simard, Joel D.; Nielsen, Christopher; Miller, Daniel E.
• 署名单位: Imperial College London; University of Waterloo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3497800
• 发表日期: 2025
• 页码: 2770-2777
• 关键词: dynamic scheduling; stability analysis; Output feedback; nonlinear dynamical systems; Time-varying systems; Poles and zeros; Closed loop systems; vectors; control theory; systematics; exponential stability; geometric methods; linear parameter-varying (LPV) systems

摘要

Linear parameter-varying (LPV) systems, which have dynamics that vary according to a scheduling parameter, are capable of representing a wide variety of nonlinear and time-varying dynamics. The LPV paradigm preserves well-understood linear design methods, although the stability analysis of these systems has remained difficult. In a recent paper, it is shown that under some stringent conditions, a linear continuous-time gain-scheduled output feedback controller can be designed to provide closed-loop exponential stability; however, the conditions are hard to check, few examples are provided and all of the examples are stable. The goal of this article is to construct two large families of single-input single-output second-order systems, which satisfy these constraints while admitting wide ranges of parameter variation. The classes constructed include unstable and nonminimum phase systems, and consequently, this work facilitates the design of exponentially stabilizing LPV controllers for systems that are difficult to control.