Error in steady state and transition, deterministic model

I am solving a deterministic growth model with two capital goods. I wrote a matlab code to solve the steady state and a dynare code to solve the transition after a permanent shock. My dynare code get the same steady state as my matlab code. However, the transition path failed with “Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 2.002503e-52.”

I then put check after command steady and it gives:

Modulus Real Imaginary

      0.9696           0.9696                0
       1.064            1.064                0
         Inf              Inf                0
         Inf              Inf                0
         Inf              Inf                0

There are 4 eigenvalue(s) larger than 1 in modulus
for 3 forward-looking variable(s)

The rank condition ISN’T verified!

mod file is attached. could someone please help me? Thanks.
main_dynare.mod (1.27 KB)

Focus on the Blachard-Kahn problem. There is most probably still a timing problem somewhere (or a mistake in your parameterization)