I am interested in an ARMA$(2,2)$ model with an additional input variable, which I want to put in state-space form. If $w_t$ is white noise, and $x_t$ is a known input, the model is given by:
$$y_t = \beta_0 + \beta_1 \cdot x_{t-1} + \alpha_1 \cdot y_{t-1} + \alpha_2 \cdot y_{t-2} + w_t + \theta_1 \cdot w_{t-1} + \theta_2 \cdot w_{t-2}.$$
Can someone please show how to write this in state-space form?
