Finite time stability analysis of the linear time-varying systems
CHEN Zhi-hua
XIE Yong-chun
Abstract：Considering the problem of the finite time stability analysis of the general nonlinear time-varying system with its initial time varying in a finite interval of time, the paper proposes the concepts of uniform finite time stability, uniform contractive stability and uniform contractive stability with fixed settling time,respectively. For a class of linear time-varying(LTV)systems,by computing the envelope of all of its trajectories,the corresponding sufficient and necessary decision theorems for its contractive stability, contractive stability with fixed settling time, uniform finite time stability, uniform contractive stability and uniform contractive stability with fixed settling time are derived respectively. Moreover, three sufficient decision theorems for the uniform contractive stability and uniform contractive stability with fixed settling time of the LTV systems are also proposed.Further,the obtained theorems are generalized to the periodic LTV system,and the generalized results provide theoretical basis for deciding the uniform finite time stability,uniform contractive stability and uniform contractive stability with fixed settling time of the periodic LTV system with respect to arbitrary initial time. Finally,four numerical examples and an example about relative motion process of two spacecraft are given to verify the correctness of the obtained results.
Keywords：linear time-varying systemuniformfinite time stabilitycontractive stabilitysettling timeenvelope
Publication Date：2018-01-01
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：12( 485-496 )