# Representation power of State Space Models

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?

• What is LTI? Also, how do you define representation power; does it reflect the generality of representation (how large the variety of processes representable in this way is)? – Richard Hardy Aug 16 '16 at 11:57
• LTI is linear time invariant. I mean can we represent all linear time invariant systems in this representation? How about nonlinear systems? – sisaman Aug 16 '16 at 13:08