An Intelligent Digital Redesign Approach to the Sampled-Data Fuzzy Observer Design

Based on the intelligent digital redesign (IDR) technique, this article proposes a novel method for designing a sampled-data fuzzy observer estimating a state vector of a nonlinear oscillating system. The proposed method guarantees not only the state estimation performance but also the state matching performance of the designed sampled-data fuzzy observer. The state matching aims at making the difference between the state trajectories of a redesigned sampled-data fuzzy observer and the given continuous-time fuzzy observer small enough. Thus, it is assumed that the continuous-time fuzzy observer was appropriately designed in advance. To solve the IDR problem, we propose the linear-matrix-inequality-based design condition that simultaneously guarantees both the state estimation performance and the state matching performance. In addition, the conservativeness of the design condition is relaxed by developing a novel integral inequality condition and a fuzzified time-dependent Lyapunov–Krasovskii functional. Finally, the superiority of the proposed methodology is demonstrated by showing the state estimation performance and the state matching performance.