We can represent subclass of linear time invariant (LTI) systems with State Space Representation:
$$\dot X = AX + BU,$$ $$Y = CX + DU.$$
Also, nonlinear systems are formulated with generalized State Space Representation where the functions could be nonlinear:
$$\dot X=f(X,U,t),$$ $$Y = g(X,U,t).$$
The question is, what is their representation power? Can we formulate any system in State Space Model?