A New Scheme of Fault Detection for Linear Discrete Time-Varying Systems

Abstract

In this note, a new scheme of fault detection (FD) is proposed for linear discrete time-varying (LDTV) systems subject to $l_{2}$ -norm bounded unknown inputs. The basic idea is to find an optimal estimation of the $l_{2}$ -norm of the unknown inputs including the unknown initial state variables. This leads to a natural design of the FD system with the $l_{2}$ -norm boundedness of the unknown inputs as a threshold and the $l_{2}$ -norm of the unknown input estimate as the evaluation function. To avoid heavy computational burden, projection technique in Krein space is applied which allows a recursive computation of the evaluation function. It is shown that the achieved FD system satisfies both the worst case and best case sensitivity/robustness ratio criteria and further applications to observer-based FD lead to an alternative design of $H_{\infty}/H_{\infty}$ and/or $H_{-}/H_{\infty}$ fault detection filter.