In this paper, a robust adaptive fuzzy controller is proposed to improve the robustness and position tracking of a MEMS gyroscope sensor. The proposed controller is designed as an indirect adaptive fuzzy controller with a supervisory compensator. It incorporates a fuzzy inference system with an adaptive controller in a unified Lyapunov framework, which can approximate and compensate for the unknown system dynamics and nonlinearities in the MEMS gyroscope. The parameters of the membership functions in the fuzzy controller can be adjusted online based on the Lyapunov method. Moreover, a supervisory controller is employed to guarantee the asymptotic stability of the closed-loop system and boundedness of the state variables in the MEMS gyroscope model. Numerical simulations demonstrate the proposed robust adaptive fuzzy controller has satisfactory tracking performance and robustness in the presence of external disturbances.

New bounds are found for the reliability of consecutive-k-out-of-n:F systems with equal component failure probabilities. The expressions involved are simple, thus allowing a direct use in the derivation of theoretical properties.

These bounds can also be employed in numerical computations when the value of n or k is so large that the exact calculation of the reliability is not achievable. Comparisons show that the approximation errors exhibited by these new formulas are lower than those of other widely used bounds.