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Positive definite function,semi-definite functions

  1. Nov 2, 2012 #1
    Hello all!
    *please explain the terms 'positive definite function' and 'semi-definite function'.*
    CONTEXT:
    I am reading a book on the stability analysis of non-linear models.
    In the chapter for 'neighborhood stability analysis',I came across the "Lyapunov function V".

    V has the following properties:
    1.V is positive definite.
    2.dV/dt is negative semi-definite(stable valley)
    3.dV/dt is positive semi-definite(unstable valley)

    I understand the usual hilltop valley visualization,but please explain the terms 'positive definite function' and 'semi-definite function'. Any level of math is understandable.
    **Is there a connect between 'positive definite function' and 'positive definite matrix'?**
     
    Last edited: Nov 2, 2012
  2. jcsd
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