NonLinear System

Definition

$$\dot{x} = f(x(t),u(t))$$

where $x(t) \in \mathbb{R}^{n}$ is the system state, $u(t) \in \mathbb{R}^{m}$ is the system input, and $f: \mathbb{R}^{n} \times \mathbb{R}^{m} \rightarrow \mathbb{R}^{n}$ is sufficiently smooth.

Example

$$\begin{bmatrix} \dot{x}_{0} \\ \dot{x}_{1} \end{bmatrix} = \begin{bmatrix} x_{1} + u \\ (1- x_{0}^{2}) x_{1} -x_{0} \end{bmatrix}$$