Bound on Amplitude of a MEMS Resonator by Approximating the Derivative of the Lyapunov Function in Finite Time

Abstract

We propose a methodology to obtain the amplitude of a nonlinear differential equation that may not satisfy Lyapunov’s global stability criterion. This theory is applied to the MEMS resonator which has a high-quality factor. The derivative of the Lyapunov function approximated for a finite time and an optimization problem was formulated. The local optima were obtained using the Karush–Kuhn–Tucker conditions, for which the amplitude was analytically formulated. The obtained amplitude, when compared with that by the numerical method, showed the validity of the analytical approximation for a useful range of the nonlinearity, but accurate only at an excitation frequency [Formula: see text]. This methodology will be useful to approximate the damping in a system if one obtains the amplitude from the experimental data near this excitation frequency.