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MEMS gyroscopes are typically designed to measure angular rate of rotation. A measurement of the angle itself is useful in many applications but cannot be obtained by integrating the angular rate due to the presence of bias errors which cause a drift. This paper presents an innovative design for a vibrating gyroscope that can directly measure both angle and angular rate. The design is based on the principle of measuring the angle of free vibration of a suspended mass with respect to the casing of the gyroscope. Several critical challenges have to be handled before the theoretical sensing concept can be converted into a reliable practical sensor. These include compensating for the presence of dissipative forces, mismatched springs, cross-axis stiffness and transmission of rotary torque. These challenges are addressed by the development of a composite nonlinear feedback control system that ensures that the mass continues to behave as a freely vibrating structure. Theoretical analysis and simulation results presented in the paper show that the gyroscope can accurately measure both angle and angular rate for low bandwidth applications.