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Equivalent Circuit Modeling

Representing the complex, time-varying behavior of the converter using simplified, lumped-element circuits (inductors, capacitors, resistors) that capture the essential dynamics for analysis.
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The statement of the theorem

The system dynamics are modeled by applying Kirchhoff's laws to lumped elements. For a general circuit, the state vector x⃗\vec{x} comprises capacitor voltages v⃗c\vec{v}_c and inductor currents i⃗L\vec{i}_L. The governing equations take the form: C⃗dv⃗cdt=I⃗source−G⃗v⃗c−i⃗L\vec{C} \frac{d\vec{v}_c}{dt} = \vec{I}_{source} - \vec{G}\vec{v}_c - \vec{i}_L and di⃗Ldt=1L(Vin−Ri⃗L−switching terms)\frac{d\vec{i}_L}{dt} = \frac{1}{L} (V_{in} - R \vec{i}_L - \text{switching terms}) where C⃗\vec{C} and L⃗\vec{L} are diagonal matrices of capacitance and inductance.