Abstract
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.
Highlights
Recent years have witnessed extensive attention on two-dimensional (2-D) systems due to the massive amount of applications in practice, for instance, multi-dimensional digital image processing [1], signal processing [2], digital filtering [3] and repetitive process [4]
This paper proposes a finite-frequency fault estimation method for two-dimensional FM systems
Utilizing the generalized KYP lemma, this problem has been recast into a multi-objective optimization problem, which is non-convex in essence
Summary
Recent years have witnessed extensive attention on two-dimensional (2-D) systems due to the massive amount of applications in practice, for instance, multi-dimensional digital image processing [1], signal processing [2], digital filtering [3] and repetitive process [4]. Due to its important engineering background, 2-D systems are still one of the research hotspots in the field of control. Many research results on 2-D systems have been developed. In [5], the authors have investigated the stability analysis of positive 2-D systems with time delays. The authors in [6] have studied the stability analysis of the 2-D nonlinear systems. On this basis, an H∞ state feedback controller has been designed to solve the stabilization problem. The model reduction problem of 2-D systems over finite-frequency ranges has been studied in [7], where a novel finite-frequency method has been proposed to replace the full frequency method. The authors in [8] have investigated the problem of asynchronous H∞
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