Fault estimation for periodic piecewise T-S fuzzy systems

This article addresses the fault estimation problem for continuous-time periodic piecewise T-S fuzzy systems affected by both faults and disturbances for the first time. Rather than conventional time-invariant results on fuzzy systems, a fault estimation observer with periodic time-varying observer parameters is developed. By constructing the Lyapunov function with periodic time-varying Lyapunov matrices, the asymptotic stability and (Formula presented.) - (Formula presented.) (energy-to-peak) performance are investigated for the augmented error dynamic systems with relaxation on the detectability assumption of all subsystems. Fault estimation observer parameters are obtained by solving the linear matrix inequality conditions which are derived by dealing with matrix polynomials. The effectiveness and conservatism reduction of the proposed method are verified by numerical examples.