Fuzzy unknown input observer-based robust fault estimation design for discrete-time fuzzy systems

• This paper aims at designing a fuzzy unknown input observer (FUIO) for fault estimation which is strictly robust against such external disturbances.
• In this paper, we propose a FUIO design method to estimate accurately the fault for discrete-time T–S fuzzy systems in the presence of disturbances.
• The advantages and novelties of this paper are as follows: First, a FUIO is proposed for discrete-time T–S fuzzy systems to achieve fault estimation, which is unaffected by the effect of the external disturbance.
• Second, by using the finite-frequency-based design technique, sufficient conditions of FUIO are proposed to calculate the gain matrices of FUIO, which is less conservative than an entire-frequency spectrum design.

This paper investigates the problem of fuzzy unknown input observer (FUIO)-based fault estimation for discrete-time Takagi–Sugeno fuzzy systems. Firstly, an augmented system description is given. Then a FUIO is proposed to achieve fault estimation, which is robust against the effect of the external disturbance. Furthermore, a less conservative FUIO design method is proposed by using a finite-frequency range technique instead of an entire-frequency method. The gain matrices of the FUIO are obtained by solving linear matrix inequalities. Finally, simulation results of a discrete-time nonlinear system are presented to illustrate the effectiveness of the proposed strategy.