On stability of linear switched differential algebraic equations

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On stability of linear switched differential algebraic equations
Abstract— This paper studies linear switched differential algebraic equations (DAEs), i.e., systems defined by a finite family of linear DAE subsystems and a switching signal that governs the switching between them. We show by examples that switching between stable subsystems may lead to instability, and that the presence of algebraic constraints leads to a larger variety of possible instability mechanisms compared to those observed in switched systems described by ordinary differential equations (ODEs). We prove two sufficient conditions for stability of switched DAEs based on the existence of suitable Lyapunov functions. The first result states that a common Lyapunov function guarantees stability under arbitrary switching when an additional condition involving consistency projectors holds (this extra condition is not needed when there are no jumps, as in the case of switched ODEs). The second result shows that stability is preserved under switching with sufficiently large dwel...
Daniel Liberzon, Stephan Trenn
Added 21 Jul 2010
Updated 21 Jul 2010
Type Conference
Year 2009
Where CDC
Authors Daniel Liberzon, Stephan Trenn
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