TABLE OF CONTENTS Let us consider the application of the above design methodology to the problem of switching controller design for a boost DC-to-DC converter circuit as shown in Fig. 7.3.
By Kirchhoff's voltage law we have E = V L when the transistor is ON and E = V L + V out when the transistor is OFF; hence, we get
where the state of the ideal switches (transistor and diode) is represented by the control variable u and u ? {0,1}.
The voltage drop V L across an inductor is given by 
, where I L is the current through the inductor with inductance L. We have 
for the voltage drop V C across a capacitor, where I C is the current through the capacitor with capacitance C. By Ohm's law, the voltage drop V R across a resistor is given by V R = RI R, where I R is the current through the resistor with resistance R. By KirchhofF's current law we get I Lu = I C + I R. Denote x 1 = I L, x 2 = V C. By taking into account that V R = V C = V out, we obtain the bilinear switched...
