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.


  • \$\begingroup\$ 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 \$\endgroup\$ – jramsay42 Feb 8 '18 at 11:42
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    \$\begingroup\$ 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. \$\endgroup\$ – Rodrigo de Azevedo Feb 9 '18 at 5:24

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