Finite-horizon H∞ fault estimation for linear time-delay systems

This paper investigates the finite-time H_∞ 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_∞ fault estimation is converted into a minimum problem of certain quadratic form. Then we introduce an stochastic system in Krein space, a sufficient and necessary condition for the minimum is derived by applying innovation analysis approach and projection theory. Finally a solution to the H_∞ fault estimation is obtained by recursively computing a partial difference Riccai equation, which has the same dimension as the original system. Compared with the conventional augmented approach, the solving of an high dimension Riccati equation is avoided.