$$\begin{align*} x_1(t+1) &=\left(\dfrac{x_1(t)}{1+x_1^2(t)}+1\right)\sin{x_2(t)} \\ x_2(t+1) &=x_2(t)\cos{x_2(t)}+x_1(t)e^{-((x_1^2(t)+x_2^2(t))/8} + \dfrac{u^3(t)}{1+u^2(t)+0.5\cos{x_1(t)+x_2(t)}} \\ y(t) &=\dfrac{x_1(t)}{1+0.5\sin{x_2(t)}}+\dfrac{x_2(t)}{1+0.5\sin{x_1(t)}}+e(t), \end{align*}$$

where $e(t)$ is the noise term, has a variance of 0.1.

$$\begin{align*} y(t) &= y(t-1) + u(t-1) + 1.3u(t-2) + 0.3u(t-1)y(t-1) \\ &+0.5u(t-2)y(t-2)+e(t)/\Delta, \end{align*}$$

where $e(t)$ is normal school white noise signal with covariance 0.1.

The system has two inputs and two outputs and is described by the following set of equations:

$$\begin{align*} y_1(k)&=0.21y_1(k-1)-0.12y_2(k-2)+0.3y_1(k-1)u_2(k-1) \\ &-1.6u_2(k-1)+1.2u_1(k-1)\\ y_2(k)&=0.25y_2(k-1)-0.1y_1(k-2)-0.2y_2(k-1)u_1(k-1) \\ &-2.6u_1(k-1)-1.2u_2(k-1). \end{align*}$$