*Appendix A.1. Proof of Proposition 1*

**Proof.** From Theorem 4.7 in [40], if any eigenvalue of the Jacobian matrix has a positive real part in some operating point, then such an operating point is Lyapunov-unstable. Consider *u*<sup>1</sup> → 0 such that the equilibrium point is *i<sup>e</sup>* → *P*/*E*, *v<sup>e</sup>* → *E*. The Jacobian matrix at this operating point is:

$$J \approx \begin{bmatrix} 0 & -\frac{1}{L} \\ \frac{1}{C} & \frac{P}{CE^2} \end{bmatrix} \tag{A1}$$

where *d*(*sign*(*x*))/*dt* = *δ*(*x*) is used, and *δ* is the Dirac's delta function. The eigenvalues of *J* are:

$$
\lambda\_{1,2} \approx \frac{PL \pm \sqrt{L^2 P^2 - 4LCE^4}}{2LCE^2} \tag{A2}
$$

of which, at least one has a positive real part with *P*, *L* > 0, demonstrating instability of the operating point.
