# Nonlinear system general representation

I am fairly new with non linear systems. I understand that a general representation of a nonlinear system is: $$\dot{x} = f(x) + g(x)\cdot u$$

where $x$ is the state variable, and $u$ the input. My question is rather general: can $f(x)$ be just a constant? Example: would it be possible to have:

$$\dot{x} = 3 + 2x\cdot u$$

Thank you very much for your help.

Lello

• Yeah that's fine, as long as you can't separate what depends on state and what depends on input it's still non-linear – jramsay42 Feb 8 '18 at 11:42
• That is not a general representation of a nonlinear system. It is the general representation of a finite-dimensional dynamical system whose dynamics are (possibly) nonlinear in state and linear in input. – Rodrigo de Azevedo Feb 9 '18 at 5:24