Asynchronous fault detection filtering design for continuous-time T-S fuzzy affine dynamic systems in finite-frequency domain

This paper investigates the problem of asynchronous fault detection filtering design for continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems in finite-frequency domain. The objective is to design an admissible piecewise affine filter such that the asymptotic stability of the filtering error system with the prescribed finite-frequency H₋/H_∞ performance can be guaranteed. It is assumed that the premise variables of the plant are unmeasurable so that the filter state transition and the plant state transition may be asynchronous. By applying the celebrated S-procedure, the generalized Kalman-Yakubovič-Popov lemma is extended such that the finite-frequency H₋/H_∞ performance of the fuzzy affine filtering error system is ensured. Furthermore, by utilizing piecewise quadratic Lyapunov functions, Projection lemma, and some matrix inequality linearization techniques, the finite-frequency fault detection filtering design approach is developed for the concerned T-S fuzzy affine dynamic system. It is shown that sufficient conditions for the existence of the fault detection filter are formulated as feasibility of a set of linear matrix inequalities. Finally, the effectiveness and advantages of the proposed design approach are illustrated by simulation studies.