Interval Observer Based Fault Detection for Lipschitz Nonlinear Systems Under Ellipsoidal Analysis

Abstract

This study devotes itself to the issue of fault detection for a class of discrete-time Lipschitz nonlinear systems by virtue of a set of restricted frequency-domain specifications. First of all, unlike traditional Luenberger-like observers, which only contain a unitary parameter matrix, a novel, more design–degree of freedom incorporated fault detection observer (FDO) under linear-matrix-inequality (LMI) conditions is innovatively constructed to access a more flexible practical adjustment range. And the evaluations of both fault sensitivity and disturbance robustness were quantified via finite-frequency $H_{\_}$ and $L_{\infty }$ indices, respectively. Besides, the actuator and sensor faults were concurrently addressed in a more wide circumstance, where the reformulated Lipschitz property is utilized to handle what the complex nonlinear term causes. Furthermore, a novel, less computational dynamic threshold based on the ellipsoidal set-membership technique was creatively synthesized during timely fault detection so as to guarantee a smaller range of residual intervals. Finally, simulation examples were conducted to demonstrate the viability and validity of the proposed strategy.