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Power Converters with Digital Filter Feedback Control by Keng C. Wu

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Appendix A

State Space Averaging

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

x˙=A1x+B1E1,y=C1Tx,0<t<dT

image(A.1)

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

x˙=A2x+B2E2,y=C2Tx,dT<t<T

image(A.2)

For switch-mode converters, the power source often remains one and the same; E1 = E2 = E. Superscript T associated with column matrix C1 and C2 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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