<inline-formula> <tex-math notation="LaTeX">$H_{\infty }$</tex-math> </inline-formula> Fault Detection for Networked Mechanical Spring-Mass Systems With Incomplete Information

Abstract

This paper focuses on the $H_{\infty }$ fault detection (FD) problem for spring-mass systems (SMSs) over networks with distributed state delays, random packet losses, sensor saturation as well as multiplicative noises via unreliable communication channels. The output measurements are affected by sensor saturation which is described by sector-nonlinearities. The multiplicative noises are described as a form of Gaussian white noises multiplied by the states. A series of stochastic variables are introduced to describe the randomly occurring distributed state delays. Random packet losses are also introduced in unreliable communications. The purpose of this paper is to design an FD filter such that: 1) The FD dynamic system is exponentially stable in the mean square. 2) The error between the fault signal and the residual signal is controlled to the minimum. 3) The optimal $H_{\infty }$ filtering performance index is achieved. A sufficient condition for the FD filter design is derived in terms of the solution to a linear matrix inequality (LMI). When the LMI has a feasible solution, the explicit parameters of the desired FD filter can be obtained. Finally, a simulation experiment is illustrated to show the effectiveness and application of the designed method.