Quadratic stability of non-linear systems modeled with norm bounded linear differential inclusions
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symmetry-12-01432.pdf
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Author(s)
Rehman, Mutti-Ur
Alzabut, Jehad
Hyder, Arfan
Date Issued
August 2020
Journal
Symmetry
Publisher
Multidisciplinary Digital Publishing Institute
Citation
Rehman, Mutti-Ur, Jehad Alzabut, and Arfan Hyder. "Quadratic stability of non-linear systems modeled with norm bounded linear differential inclusions." Symmetry 12, 9 (August 2020): 1432 ©2020 Author(s)
Version
Final published version
Abstract
In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum of perturbed system which guarantees the stability of non-linear dynamical system. KEYWORDS: quadratic stability; Lyapunov function; gradient system of ODE's; bounded linear differential inclusion
MIT Department
Massachusetts Institute of Technology. Department of Chemical Engineering
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DOI of Published Version
https://doi.org/10.3390/sym12091432
