Finite-time stability analysis of a class of nonlinear time-varying systems: a numerical algorithm. Issue 10 (27th July 2018)

• Record Type: Journal Article
• Authors: Chen, Zhihua; Xie, Yongchun
• Is Part Of: International journal of systems science. Volume 49:Issue 10(2018)
• Page Start: 2224
• Page End: 2242
• Publication Date: 2018-07-27
• Subjects: Finite-time stability -- nonlinear system -- time-varying system -- generalised Gronwall–Bellman inequality -- numerical algorithm; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2018.1496299
• Languages: English
• ISSNs: 0020-7721

Abstract

ABSTRACT: The paper investigates the finite-time stability (FTS) analysis of a very general class of nonlinear time-varying systems. The FTS of the considered system, whose vector field consists of a nonlinear part which can be sublinear or superlinear, and a linear part which can be time-varying, has not been fully studied before. By estimating the bound of the norm of the considered system's states with the generalised Gronwall–Bellman inequality, a sufficient criterion is established to guarantee the FTS of the considered system. To facilitate checking the criterion in practice, a novel numerical algorithm is proposed by numerically solving certain differential equations. Therefore, the FTS of the considered class of nonlinear time-varying systems can be easily analysed by the numerical algorithm. Further considering the numerical errors in the practical numerical computation, we strictly prove the credibility and programmability of the numerical algorithm in theory. Finally, three numerical examples are provided to illustrate the effectiveness the proposed results.