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Hybrid Dynamical Systems: Modeling, Stability and Interconnection

Hybride Dynamische Systeme: Modellierung, Stabilität und Zusammenschaltung

Please always quote using this URN: urn:nbn:de:bvb:20-opus-190993
  • This work deals with a class of nonlinear dynamical systems exhibiting both continuous and discrete dynamics, which is called as hybrid dynamical system. We provide a broader framework of generalized hybrid dynamical systems allowing us to handle issues on modeling, stability and interconnections. Various sufficient stability conditions are proposed by extensions of direct Lyapunov method. We also explicitly show Lyapunov formulations of the nonlinear small-gain theorems for interconnected input-to-state stable hybrid dynamical systems.This work deals with a class of nonlinear dynamical systems exhibiting both continuous and discrete dynamics, which is called as hybrid dynamical system. We provide a broader framework of generalized hybrid dynamical systems allowing us to handle issues on modeling, stability and interconnections. Various sufficient stability conditions are proposed by extensions of direct Lyapunov method. We also explicitly show Lyapunov formulations of the nonlinear small-gain theorems for interconnected input-to-state stable hybrid dynamical systems. Applications on modeling and stability of hybrid dynamical systems are given by effective strategies of vaccination programs to control a spread of disease in epidemic systems.show moreshow less
  • Entwicklung eines Frameworks für hybride dynamische Systeme zur Decomkosition oder Komposition solcher Systeme. Untersuchung der Stabilität von gekoppelten hybriden Systemen.

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Author: Ratthaprom PromkamORCiD
URN:urn:nbn:de:bvb:20-opus-190993
Document Type:Doctoral Thesis
Granting Institution:Universität Würzburg, Fakultät für Mathematik und Informatik
Faculties:Fakultät für Mathematik und Informatik / Institut für Mathematik
Referee:Prof. Dr. Sergey DashkovskiyORCiD
Date of final exam:2019/07/26
Language:English
Year of Completion:2019
DOI:https://doi.org/10.25972/OPUS-19099
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
GND Keyword:Dynamical system; Stability; Hybridsystem; Interconnection
Tag:Dynamical Systems; Hybrid Dynamical Systems; Lyapunov Stability; Small-Gain Theorem
MSC-Classification:93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Dxx Stability / 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, Lp; lp, etc.)
Release Date:2019/11/08
Licence (German):License LogoCC BY-NC-SA: Creative-Commons-Lizenz: Namensnennung, Nicht kommerziell, Weitergabe unter gleichen Bedingungen 4.0 International