Proportional Multiple Integral Observer-based Fault Estimation for Takagi-Sugeno Fuzzy Systems with Interval Time-varying Delay

This article studies the fault estimation problem of T-S fuzzy systems with interval time-varying delay, actuator fault, sensor fault and external disturbance. The designed Proportional Multiple Integral (PMI) observer can estimate system states, sensor and actuator fault simultaneously. A new Lyapunov-Krasovskii function that fully considers the upper and lower bounds of the time delay is constructed to prove the proposed method. In order to get the gain matrices of the designed PMI observer, one sufficient condition for the existence of the fault estimation observer is given in form of Linear Matrix Inequality (LMI). By introducing
$H_{\infty}$
performance index, the influence of external disturbance on fault estimation is suppressed. A numerical example is proposed to verify the effectiveness of the proposed method.