Appendix A

While dwelling in one structure in the time frame of dT, the state equation and the output are described by

$\dot{x}={A}_{1}x+{B}_{1}{E}_{1},\text{\hspace{1em}}y={{C}_{1}}^{\text{T}}x,\text{\hspace{1em}}0<t<dT$

(A.1)

In the rest-time duration (1 − d)T, both equations change since structure varies.

$\dot{x}={A}_{2}x+{B}_{2}{E}_{2},\text{\hspace{1em}}y={{C}_{2}}^{\text{T}}x,\text{\hspace{1em}}dT<t<T$

(A.2)

For switch-mode converters, the power source often remains one and the same; E_{1} = E_{2} = E. Superscript T associated with column matrix C_{1} and C_{2} stands for “Transposition” and is not to be confused with switch period T.

State space average proposed a view that under ...

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