Lyapunov and external stability of Caputo fractional order switching systems. (November 2019)

• Record Type: Journal Article
• Authors: Wu, Cong; Liu, Xinzhi
• Is Part Of: Nonlinear analysis. Volume 34(2019)
• Page Start: 131
• Page End: 146
• Publication Date: 2019-11
• Subjects: Lyapunov stability -- External stability -- Caputo fractional order switching system -- Quadratic function -- Diffusive realization; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2019.06.002
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: This paper investigates Lyapunov and external stability of Caputo fractional order switching systems. It proves an estimation for the Caputo fractional order derivative of an arbitrary quadratic function whose variable is a function of time with the same differential properties as those given by the most recent smoothness result, and then establishes criteria on Lyapunov stability that bridge over existing difficulties. On the other hand, the equivalence between Caputo fractional order switching control systems and their diffusive realizations is shown. This together with a Lyapunov-like function proven to be well defined shows their advantages in solving the problem of external stability.