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System of nonhomogeneous difference equation

  1. Nov 6, 2009 #1
    How do you solve the system z(t+1)=Az(t)+b where A is a 2x2 matrix and z(t+1), z(t), b are 2x1 matricies?
    I solved the homogeneous solution: z(t)=P(D^t)(P^-1)z(0) where D is the diagonal matrix of eigenvalues of A and P is the matrix of eigenvectors.
    I tried to solve the nonhomogeneous solution at the steady state where z(t+1)=z(t). I'm not sure if this is the right method.
    Then I added the two solutions z(t) for the homogeneous and the nonhomogeneous equations.
     
  2. jcsd
  3. Nov 7, 2009 #2
    Guess a constant vector for the particular solution. This will give
    [tex]x_{p}=(I-A)^{-1}b[/tex]
    Then add it to the homogeneous solution to obtain the solution.
     
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