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This paper discusses the problem of fault estimation for two-dimensional (2-D) Fornasini-Marchesini (FM) dynamical systems. The objective of this paper is to design a fault estimation filter to reconstruct the characteristics of faults in low-frequency domain and satisfy different performance levels. Utilizing the generalized Kalman-Yakubovich-Popov (GKYP) lemma, this problem is transformed into a multi-objective optimization problem, which is non-convex in essence. On this basis, an optimization algorithm is proposed to solve the non-convex optimization problem. Sufficient conditions are derived for the proposed fault estimation filter. Finally, simulation results show the effectiveness of the theoretical results.

Fault Estimation Filter Design for Two-Dimensional Fornasini-Marchesini Dynamical Systems in Low-Frequency Domain