A methodology for the identification of linear dynamical systems and non-linear state space for multivariable systems. Mathematical models are developed only obtained using linear algebra techniques to input and output data to identify system is presented. The methodology applied to the data, allow to obtain a state space model to the discrete-time linear and extending jointly with kernels, to identify non-linear systems, based on the use of a non-linear function to the input and output of the linear model generating the system dynamics.