Robust $H_\infty$ Filtering for Two-Dimensional Uncertain Linear Discrete Time-Varying Systems: A Krein Space-Based Method

A robust H
_∞
filtering algorithm is proposed for two-dimensional (2-D) linear uncertain time-varying systems in this study. The considered 2-D systems are subject to unknown inputs, measurement noises, and time-varying modeling uncertainties. To appropriately deal with the system uncertainties, a new problem formulation of robust H∞ filter design for 2-D uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard H
_∞
performance index. Then, the robust 2-D H
_∞
filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions. By relating this quadratic form to a specific 2-D state-space model in Krein space, the Krein space estimation theory is used to solve the reformulated optimization problem. A recursive robust 2-D time-varying H
_∞
filter and its explicit condition for the existence are obtained through projection techniques in 2-D Krein space. One thermal process plant is used to illustrate the effectiveness of the proposed filter.