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Title: Uniform asymptotic and input to state stability by indefinite Lyapunov functions
Authors: Şahan, Gökhan
Özdemir, Durmuş
Keywords: Input-to-state stability
Lyapunov function
Nonlinear time-varying systems
Uniform asymptotic stability
Uniform stability
Asymptotic stability
Publisher: Elsevier
Abstract: In this work, we study uniform, uniform asymptotic, and input-to-state stability conditions for nonlinear time-varying systems. We introduce an easily verifiable condition for uniform attractivity by utilizing an indefinite sign upper bound for the derivative of the Lyapunov function. With this bounding structure, we propose novel conditions that enable us to test uniform stability, uniform asymptotic stability, and ISS, easily. As a result, the constraints on the coefficients of the bound that identify uniformity for stability and attractivity, and many of the available conditions have been relaxed. The results are also used for the perturbation problem of uniformly stable and uniformly asymptotically stable linear time-varying systems. Consequently, we demonstrate that uniform asymptotic stability of nonlinear time-varying systems can be robust for perturbations, but with special time-varying coefficients. © 2024 European Control Association
ISSN: 0947-3580
Appears in Collections:Mathematics / Matematik
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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