This paper presents a new adaptive control algorithm to control the sense axis of a Z-axis MEMS gyroscope. A force-to-rebalance mode of operation is applied to the sense axis. Under this mode, the output amplitude of sense axis is continuously monitored and driven to zero by the controller while an input rotation rate is measured. Adaptive laws are developed to estimate the rotation rate and a quadrature error term caused by mechanical imperfection. In the paper, we suppose the rotation rate of the gyroscope is an unknown time-varying piecewise continuous parameter, rather than a constant as in current literature. A Lyapunov approach is applied to obtain both control and adaptive laws. © 2006 IEEE.