Stability of a dual-axis vibratory MEMS gyroscope that is subject to periodic fluctuations in input angular rates is investigated. For the purpose of acquiring stability conditions, when the angular rate input is subject to small intensity periodic fluctuations, dynamic behavior of periodically perturbed linear gyroscopic systems is studied in detail. An asymptotic approach based on the method of averaging has been employed for this purpose, and closed-form conditions for the onset of instability due to parametric resonances have been obtained for this type of vibrating gyroscope. Furthermore, for characterizing the effect due to change in angular rate input, an in-depth natural frequency analysis has been performed. Stability predictions have been illustrated via plots in the excitation amplitude-frequency space. Based on these results, the dangerous critical frequencies can be avoided in the design to achieve a high performance.

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