Interval Observer-Based Fault Isolation for Discrete-Time Fuzzy Interconnected Systems With Unknown Interconnections

This paper is concerned with the fault isolation problem for discrete-time fuzzy interconnected systems with unknown interconnections. First, for each subsystem, a fault isolation interval observer is constructed by taking into account the bounds of the unknown interconnections and subsystem disturbances. Then, l
₁
and H
_∞
performances are introduced to improve the tightness of the residual intervals and the sensitivity to their own faults, respectively. Furthermore, the fault isolation decision is made by determining whether the zero value is excluded from each residual interval. By utilizing the piecewise Lyapunov functions and dilated linear matrix inequalities, the obtained observer design conditions are less conservative than the existing results with the common and diagonal Lyapunov functions. Finally, simulation results are presented for showing the effectiveness and superiority of the proposed method.