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I'm wondering, if we have a nonlinear system governed by

$\dot{x} = Ax + g(x)$ where $||g(x)|| \leq \gamma ||x||^2$ and A is Hurwitz

how can we show that the origin is globally exponentially stable? My first thoughts are to use Lyapunov's Indirect Method but what Lyapunov candidate function would work here?

Is $V(x) = x^{T}Px + \int_0^x g(y)dy$ suitable?

Or how else can we show that the origin is globally exponentially stable?

Thanks in advance

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  • $\begingroup$ Just added the tags you specified $\endgroup$
    – Aerandir
    Commented Dec 15, 2013 at 23:30
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    $\begingroup$ Why are you so sure that your claim is true, if you don't know a proof? $\endgroup$
    – Stefan Kohl ♦
    Commented Dec 16, 2013 at 0:00

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