This paper investigates the finite-time fault estimation problem for linear time-delay systems, where the delay appears in both state and measurement equations. Firstly, the design of finite horizon 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 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.
Xinmin Song. Xuehua Yan. "Krein Space-Based Fault Estimation for Discrete Time-Delay Systems." Abstr. Appl. Anal. 2014 (SI38) 1 - 7, 2014. https://doi.org/10.1155/2014/935216