Invariance Principles and Observability in Switched Systems With an Application in Consensus

• 成果类型: Article
• 署名作者: Lee, Ti-Chung; Tan, Ying; Su, Youfeng; Mareels, Iven
• 署名单位: National Sun Yat Sen University; University of Melbourne; Fuzhou University; International Business Machines (IBM); IBM Australia; IBM Research - Australia
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3035594
• 发表日期: 2021
• 页码: 5128-5143
• 关键词: Switches; trajectory; observability; Limiting; Lyapunov methods; CONVERGENCE; Time-varying systems; Integral invariance principle; LaSalle invariance principle; leaderless consensus; switched nonlinear time-varying (NLTV) systems; weak observability

摘要

Using any nonnegative function with a nonpositive derivative along trajectories to define a virtual output, the classic LaSalle invariance principle can be extended to switched nonlinear time-varying (NLTV) systems, by considering the weak observability associated with this output. The concept of weak observability reflects the information of the limiting behavior of state trajectories hidden in the zero locus of the output. In the context of switched NLTV systems, weak observability can be explored using the recently established framework of limiting zeroing-output solutions. Adding to this, a new approach to show uniform global attractivity of a closed set (without assuming uniform Lyapunov stability or dwell-time conditions) is proposed. A further extension of the generalized LaSalle invariance principle allows the consideration of cascaded switched NLTV systems, which is used to characterize how consensus in a leaderless swarm of nonholonomic robots allowing for switching communication topologies may be established.