Boularas, Driss; Cheban, David Asymptotic stability of switching systems. (English) Zbl 1198.34012 Electron. J. Differ. Equ. 2010, Paper No. 21, 18 p. (2010). The authors first introduce shift dynamical systems on the space of piecewise constant functions and show that every switched system generates a cocycle. Necessary and sufficient conditions for asymptotic stability of switched homogeneous systems are given, a sufficient condition for the asymptotic stability of slow switched homogeneous systems is obtained. Furthermore, the authors obtain necessary and sufficient conditions for the uniform asymptotic stability of linear switched systems. Reviewer: Olusola Akinyele (Bowie) Cited in 2 Documents MSC: 34A36 Discontinuous ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34D45 Attractors of solutions to ordinary differential equations 37B55 Topological dynamics of nonautonomous systems Keywords:uniform asymptotic stability; cocycles; global attractors; uniform exponential stability; switched systems PDF BibTeX XML Cite \textit{D. Boularas} and \textit{D. Cheban}, Electron. J. Differ. Equ. 2010, Paper No. 21, 18 p. (2010; Zbl 1198.34012) Full Text: EuDML EMIS OpenURL