Krein-space based robust H_∞ fault estimation for two-dimensional uncertain linear discrete time-varying systems

In this study, the robust H_∞ fault estimation problem for two-dimensional linear time-varying systems with norm-bounded unknown input, measurement noise, and time-varying process uncertainty is investigated. By introducing an equivalent auxiliary system and a new certain indefinite quadratic form performance function, the system uncertainty can be appropriately considered into the new performance function and the fault estimator design is converted to the minimization problem of a quadratic form. Based on the partially equivalence property between the deterministic quadratic form problem and the Krein space estimation theory, the two-dimensional H_∞ fault estimation problem can be solved via signal deconvolution in Krein space. Through employing projection operation and Riccati-like difference equation in two dimensions, both the recursive form fault estimator and the explicit condition for existence of the estimator are derived. One Darboux equation example is provided to illustrate the effectiveness of the proposed fault estimator.