A Survey on Filtering Issues for Two-Dimensional Systems: Advances and Challenges

In the past few decades, both theoretical developments and practical applications of the two-dimensional (2-D) systems have received considerable research interest due to their clear engineering insights in many industrial branches. In order to estimate the actual system states from available and possibly noisy measurements, various filtering strategies have been proposed in the existing literature which include, but are not limited to, Kalman filtering, variance-constrained filtering, H ∞ filtering, l 2 - l ∞ filtering, l 1 filtering, dissipative filtering, and protocol-based filtering approaches. In particular, the filtering issues of 2-D systems subjected to disturbances/noises from different sources have drawn much research attention. The intent of this survey is to not only provide a comprehensive review of the latest results but also bestow some in-depth insights on the future research with respect to the filter design problems for 2-D systems under various performance requirements. The fundamentals of the 2-D systems are first presented and the corresponding filtering techniques are introduced from the aspects of engineering insights and physical interpretations. Then, several well-known 2-D systems are recalled and discussed, and some other 2-D systems with more complicated dynamics are surveyed. Subsequently, the recent advances in designing appropriate 2-D filtering algorithms under specific filtering performance indices are reviewed. Finally, this paper is concluded with some possible future research topics outlined on the 2-D filtering schemes.