you can linearize the non linear system of equations to a linear approximation about an equilibrium point X0 in your variable space, by using Taylor series expansion and truncation at the linear term, which involves the Jacobian of the nonlinear system evaluated at the point X0.

Dear Shahram Hosseini,

Please check the following papers on this topic (and references therein):

1)https://pdfs.semanticscholar.org/bd48/f471266a3dc2865d9a56e50ec2bbb3671664.pdf

2) https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8264032

Hope this helps.

Hi Shahram, to convert the nonlinear system into the matrix form, the nonlinear system maybe modeled as a linear parameter-varying (LPV) system. The following paper maybe helpful to you:

Cai, G., Hu, C., & Duan, G. (2011). Eigenstructure assignment for linear parameter-varying systems with applications. Mathematical and Computer Modelling, 53(5-6), 861–870. doi:10.1016/j.mcm.2010.10.023

Read this paper

https://pdfs.semanticscholar.org/bd48/f471266a3dc2865d9a56e50ec2bbb3671664.pdf