Sampled-data $$H_\infty$$ Fuzzy Observer Design Under Time-varying Sampling Rates and its Applications to the Attitude and Heading Reference System

Abstract

In this paper, we design a sampled-data \(H_\infty\) fuzzy observer for nonlinear systems under variable sampling periods. To do so, a linear matrix inequality-based design condition is derived to stabilize the error vector consisting of the difference of the state vectors of the observer and the system. When deriving the condition, we propose a time-dependent fuzzy Lyapunov–Krasovskii functional with discrete time membership functions to obtain numerically less conservative condition. Also, since the proposed method allows the sampling time to be variable, it can be used in low-cost hardwares that do not meet the strict sampling period. Finally, in the hardware experiment, the proposed method is applied to design the attitude and heading reference system that estimates the Euler angles from inertial sensor data, and the results demonstrate the effectiveness of the proposed method.