Abstract
This paper addresses the finite horizon ${H_\infty }$ fault estimation problem for 2-D linear discrete time-varying systems with bounded unknown input and measurement noise. The main contribution of this paper is the ${H_\infty }$ fault estimator for 2-D systems with a necessary and sufficient existence condition. By introducing a partially equivalent stochastic dynamic system in Krein space, the necessary and sufficient condition for the existence of the ${H_\infty }$ fault estimator is derived based on innovation analysis and projection formula in Krein space. Then, the solution of the estimator is achieved by means of a Riccati-like difference equation for 2-D systems. Finally, a thermal process example is given to demonstrate the effectiveness of the proposed method.
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