**4. Open-Loop Instability of the Boost Converter Dynamics with a CPL**

Consider the dynamic system represented by Equations (14) and (15). The following shows that an operating point of such a system can be unstable either in DCM or CCM operation.

**Proposition 1.** *At least, one operating point of the dynamic system represented by the Equations* (14) *and* (15)*, is Lyapunov-unstable for P*, *L* > 0*.*

**Proof.** See Appendix A.1.

It is worth mentioning that different operating points may be open-loop stable; however, in general, open-loop stability cannot be ensured by a constant control input. The interested reader will surely obtain parameters and constant values of *u*<sup>1</sup> for which the operating point is stable. However, the question remains whether there is a control signal *u*<sup>1</sup> capable of avoiding unstable system dynamics.
