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Average-State-Space Model

The fundamental mathematical representation of the converter's continuous-time behavior, derived by assuming the switching frequency is high. It yields a linear time-invariant (LTI) system representation: \dot{\vec{x}}(t) = \vec{A}\vec{x}(t) + \vec{B}\vec{u}(t).
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The statement of the theorem

Define the state vector x⃗(t)∈Rn\vec{x}(t) \in \mathbb{R}^n and the input vector u⃗(t)∈Rm\vec{u}(t) \in \mathbb{R}^m. The fundamental continuous-time behavior is modeled by the linear time-invariant (LTI) system: x⃗˙(t)=A⃗x⃗(t)+B⃗u⃗(t)\dot{\vec{x}}(t) = \vec{A}\vec{x}(t) + \vec{B}\vec{u}(t) where A⃗∈Rn×n\vec{A} \in \mathbb{R}^{n \times n} and B⃗∈Rn×m\vec{B} \in \mathbb{R}^{n \times m} are the system matrices.