Buck-Boost

PWM: amplitude [0; V_in], period T, duty cycle $\alpha$.

Continuous conduction when: $I_{out}\ge \frac{(1-\alpha ).\alpha .T.V_{in}}{2L}$

Discontinuous conduction when: $I_{out}<\frac{(1-\alpha ).\alpha .T.V_{in}}{2L}$

Continuous conduction: $V_{out}=\alpha .V_{in}$

Discontinuous conduction: $V_{out}=\frac{V_{in}}{1+{\displaystyle \frac{2L.I_{out}}{{\alpha }^2.T.V_{in}}}}$