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Constructing Lyapunov functions using eigenvectors

  1. Jun 6, 2013 #1
    1. The problem statement, all variables and given/known data

    How can I produce a Lyapunov function using the eigenvalues and vectors
    x'=-x+y
    y'=-x

    2. Relevant equations



    3. The attempt at a solution So I got the matrix using jacobian and I got the matrix
    -1 1
    -1 0
    then i found the eigenvalues to be λ_1= (-1+sqrt3 i)/2 and λ2= (-1-sqrt3 i)/2 and i found the eigenvectors v1= (1 1/2 +sqrt3i /2) v2= (1 1/2 -sqrt3i/2) Im not exactly sure how I can proceed further though. Im not sure how to construct Lyapunov function using this information...
     
  2. jcsd
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