A new class of strict Lyapunov functions for nonlinear time-varying systems. (February 2020)

• Record Type: Journal Article
• Authors: Zhang, Bin; Jia, Yingmin; Du, Junping
• Is Part Of: Automatica. Volume 112(2020)
• Publication Date: 2020-02
• Subjects: Strict Lyapunov functions -- Nonlinear time-varying systems -- Homogeneous auxiliary systems; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108697
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This paper focuses on strict Lyapunov functions of nonlinear time-varying systems using homogeneity-based methods. The concept of homogeneous auxiliary system is introduced. Based on the auxiliary system, a new class of strict Lyapunov functions is established. Sufficient conditions of uniform asymptotic stability are provided under the homogeneous framework. The results are extended to deal with robustness problems. It is shown that the nonlinear time-varying systems remain stable in the presence of higher order perturbing terms.