Nonlinear microelectromechanical systems (MEMS) analysis and design via the Lyapunov stability theory

This article applies the Lyapunov stability theory to microelectromechanical systems (MEMS) analysis and design. A desired level of validity and performance can be attained through synergy of nonlinear control, electromagnetics, and electromechanics. Microelectromechanical systems integrate microstructures and microdevices, and the component models are described by nonlinear deterministic/stochastic time-invariant/time-varying multivariable ordinary and partial differential equations as well as difference equations. We apply Lyapunov's stability theory. The microscale motion devices are integrated with ICs. The circuitry dynamics is very fast compared with the electromechanical transients. Therefore, the motion devices behavior has the dominant effect. Analysis and design should be performed researching electromagnetic, electromechanical and circuitry aspects. Fundamental, analytical, numerical, and experimental results are documented in this paper.