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Small-Signal Model (SSM)

A linear approximation of the converter's behavior around an operating point (DC bias). It is used for stability analysis and control design, typically represented by transfer functions or state-space matrices.
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The statement of the theorem

Linearization around the steady-state operating point (x⃗0,u⃗0)(\vec{x}_0, \vec{u}_0) yields the small-signal model (SSM) for the deviation variables Δx⃗=x⃗−x⃗0\Delta\vec{x} = \vec{x} - \vec{x}_0 and Δu⃗=u⃗−u⃗0\Delta\vec{u} = \vec{u} - \vec{u}_0: d(Δx⃗)dt=A⃗ssΔx⃗+B⃗ssΔu⃗\frac{d(\Delta\vec{x})}{dt} = \vec{A}_{ss}\Delta\vec{x} + \vec{B}_{ss}\Delta\vec{u} where A⃗ss=∂f∂x⃗∣(x⃗0,u⃗0)\vec{A}_{ss} = \left. \frac{\partial f}{\partial \vec{x}} \right|_{(\vec{x}_0, \vec{u}_0)} and B⃗ss=∂f∂u⃗∣(x⃗0,u⃗0)\vec{B}_{ss} = \left. \frac{\partial f}{\partial \vec{u}} \right|_{(\vec{x}_0, \vec{u}_0)} are the Jacobian matrices.