A general relation between the ranges of stability of electrostatic actuators under charge or voltage control

Pull-in instability is a crucial effect in electrostatically-actuated microelectromechanical devices. This phenomenon was recently shown to occur under both voltage and charge control. So far, for all known cases, it has been shown that, under charge excitation, electrostatic actuators have a larger range of stability than under voltage excitation. No counter-examples are known, and whether this is a general rule for electrostatic actuators is an open question. In this work, a general proof is presented that shows this is indeed a fundamental rule for general electrostatic actuators.