A converse Lyapunov theorem for switched DAEs | Zendy

Trenn Stephan | Zendy; Wirth Fabian | Zendy

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A converse Lyapunov theorem for switched DAEs

Author(s) -

Trenn Stephan,

Wirth Fabian

Publication year - 2012

Publication title -

pamm

Language(s) - English

Resource type - Journals

ISSN - 1617-7061

DOI - 10.1002/pamm.201210381

Subject(s) - converse , lyapunov function , mathematics , ordinary differential equation , lyapunov exponent , differential algebraic equation , ode , exponential stability , norm (philosophy) , pure mathematics , mathematical analysis , differential equation , physics , nonlinear system , law , geometry , quantum mechanics , political science

For switched ordinary differential equations (ODEs) it is well known that exponential stability under arbitrary switching yields the existence of a common Lyapunov function. The result is known as a “converse Lyapunov Theorem”. In this note we will present a converse Lyapunov theorem for switched differential algebraic equations (DAEs) as well as the construction of a Barabanov norm for irreducible switched DAEs. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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