Sliding-Mode Control With Time-Varying Sliding Surface for Linear Uncertain Impulsive Systems

• 成果类型: Article
• 署名作者: Chen, Wu-Hua; Niu, Shuning; Zheng, Wei Xing
• 署名单位: Guangxi University; Western Sydney University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3357756
• 发表日期: 2024
• 页码: 4836-4843
• 关键词: Time-varying systems; Symmetric matrices; Matrix decomposition; trajectory; switches; Lyapunov methods; impulsive systems; piecewise Lyapunov function; sliding-mode control (SMC); time-varying sliding surface

摘要

This article presents a new sliding-mode control (SMC) design method for linear uncertain impulsive systems, where the sliding function is designed to be linear with a time-varying projection matrix. When the time-varying projection matrix satisfies a so-called continuity condition, the sliding function is continuous along the state trajectories, which will facilitate the analysis and design of SMC laws. To obtain a tractable design algorithm on the time-varying projection matrix, a regular form is introduced for the representation of the considered impulsive system. Within this framework, the projection matrix is represented as a piecewise time-varying form based on a partition on the impulse intervals, which can be determined by finite constant gain matrices. Then, a piecewise Lyapunov function associated with the partition is constructed to analyze the stability of the reduced-order sliding dynamics. By this means, the solvability condition for the desired sliding function is obtained by solving a convex optimization problem. Finally, a numerical example that considers four types of impulses is provided to show the effectiveness of the proposed design scheme.