**5. Nonlinear Stabilization Controller for the Boost Converter with a CPL for CMI Operation**

This section shows that a nonlinear control law can stabilize the system represented by Equations (14) and (15). At present, stability for general nonlinear switched systems under arbitrary switching can be ensured only by a common Lyapunov function approach; see, for instance [38,39] and the references therein.

**Theorem 1.** *Let P* > 0*, v* > 0*, i* > 0*, and v* ≥ *E. The gain scheduling control law:*

$$1 - \mu\_1 = \frac{k\_1 P}{v} - k\_2 P - \frac{k\_3 \dot{v}}{v^2} - k\_4 \dot{v}\_\prime \tag{25}$$

$$\begin{aligned} \text{using for } \gamma = 1 \begin{cases} \begin{array}{l} k\_1 = \frac{3k\_3 - 12 \text{CE} Lf}{8 \text{CPI} f} \\ k\_2 > 0 \\ k\_3 > 0 \text{ (small enough)} \end{array} \\\ k\_4 = \frac{3k\_3}{8 \text{LP} f} \end{aligned} \tag{26}$$
 
$$\text{and for } \gamma = 0 \begin{cases} \begin{array}{l} k\_1 > 0 \text{ (small enough)} \\ k\_2 > \frac{1}{P} \\ k\_3 = 0 \\ k\_4 = 0 \end{cases} \end{aligned} \tag{27}$$

*stabilizes the switched system* (14) *and* (15) *for an arbitrary switching law.*
