Krein Space-Based H ∞ Fault Estimation for Discrete Time-Delay Systems

Abstract

This paper investigates the finite-time $H_{\infty }$ fault estimation problem for linear time-delay systems, where the delay appears in both state and measurement equations. Firstly, the design of finite horizon $H_{\infty }$ fault estimation is converted into a minimum problem of certain quadratic form. Then we introduce a stochastic system in Krein space, and a sufficient and necessary condition for the minimum is derived by applying innovation analysis approach and projection theory. Finally, a solution to the $H_{\infty }$ fault estimation is obtained by recursively computing a partial difference Riccati equation, which has the same dimension as the original system. Compared with the conventional augmented approach, the solving of a high dimension Riccati equation is avoided.