Robust [Formula Omitted] Filtering for Two-Dimensional Uncertain Linear Discrete Time-Varying Systems: A Krein Space-Based Method

• Published in: IEEE transactions on automatic control Vol. 64; no. 12; p. 5124
• Main Authors: Zhao, Dong, Ding, Steven X, Karimi, Hamid Reza, Li, Yueyang
• Format: Journal Article
• Language: English
• Published: New York The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 01.01.2019
• Subjects: Algorithms; Design optimization; Discrete time systems; Filter design (mathematics); Performance indices; Quadratic forms; Robustness; State space models; Two dimensional models; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2019.2908699

A robust [Formula Omitted] 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 [Formula Omitted] filter design for 2-D uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard [Formula Omitted] performance index. Then, the robust 2-D [Formula Omitted] 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 [Formula Omitted] 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.