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Boundary Condition Analysis

Applying physical constraints (e.g., continuity of current and voltage across switches) at the boundaries of the switching period. This ensures the derived model accurately reflects the physical system limits.

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The statement of the theorem

At the switching boundaries

t_k

and

t_{k+1}

, the physical continuity constraints must be satisfied. Specifically, the inductor current

i_L(t)

and capacitor voltages

v_c(t)

must be continuous:

i_L(t_{k+1}) = i_L(t_k) \quad \text{and} \quad v_c(t_{k+1}) = v_c(t_k)

These conditions are used to define the initial state for the next switching interval.