Sampling-Time-Dependent Observer Design for T-S Fuzzy Sampled-Data Systems Under Membership Function Mismatch

This study focuses on a sampled-data observer design method for a Takagi-Sugeno (T-S) fuzzy system using a sampling-time-dependent approach. The sampled-data observer dynamics are given by combining a conventional observer gain and a novel observer gain that dynamically changes within each sampling interval. To exploit the information on aperiodic sampling intervals, samplingdependent matrices are incorporated into a Lyapunov-Krasovskii functional (LKF), from which the sufficient conditions for stabilization of the estimation error dynamics and H∞ disturbance attenuation are derived in the form of linear matrix inequalities (LMIs). In addition, the mismatch between the system and the observer is regarded as a disturbance and attenuated via an H∞ performance criterion, whereas the mismatch between the continuous-time and sampled membership grades of the observer is explicitly characterized by a prescribed deviation bound and incorporated into the stability conditions using slack matrix variables. Finally, a comparative simulation example with a conventional sampled-data observer demonstrates the effectiveness, reduced conservatism, and improved estimation performance of the proposed method.