Example
Consider the following differential equation with solution x on :
Considering that |x| is always positive around the origin it is a natural candidate to be a Lyapunov function to help us study x. So let on . Then,
This correctly shows that the above differential equation, x, is asymptotically stable about the origin.
Read more about this topic: Lyapunov Function
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“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
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