title: A note on finite-time and fixed-time stability.
abstract: In this letter, by discussing ṫ(V)=μ(-1)(V), we provide a general approach to reveal the essence of finite-time stability and fixed-time convergence for the system V̇(t)=μ(V(t)). Thus, we derive some conditions for finite-time and fixed-time convergence. As applications, we propose schemes to achieve finite-time and fixed-time synchronization in complex networked systems.
authors.affiliation: Centre for Computational Systems Biology, and Laboratory of Mathematics for Nonlinear Science, School of Mathematical Sciences, Fudan University, Shanghai, China. Electronic address: wenlian@fudan.edu.cn.
authors.forename: Wenlian
authors.initials: W
authors.lastname: Lu
authors.affiliation: Department of Computer Science and Technology, Tongji University, The Key Laboratory of Embedded System and Service Computing, Ministry of Education, Shanghai 200092, China. Electronic address: xwliu@tongji.edu.cn.
authors.forename: Xiwei
authors.initials: X
authors.lastname: Liu
authors.affiliation: School of Computer Sciences, Fudan University, 200433, Shanghai, China. Electronic address: tchen@fudan.edu.cn.
authors.forename: Tianping
authors.initials: T
authors.lastname: Chen
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D013997:Time Factors
keywords: Consensus; Delay systems; Neural networks; Synchronization; Time-varying systems