Abstract

This paper investigates the finite-time H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> 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.

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