Abstract
This paper considers the problem of filter design for two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy mode. The problem to be solved in the paper is to find a H∞ filter model such that the filtering error system is asymptotically stable. A numerical example is employed to illustrate the validity of the proposed methods.
Highlights
IntroductionIn the last few decades, many researchers have investigated two-dimensional (2-D) systems including continuous, discrete and continuous-discrete settings as these systems have great applications in engineering fields such as process control, multi-dimensional digital filtering, image processing, see for instance [1–6]
In the last few decades, many researchers have investigated two-dimensional (2-D) systems including continuous, discrete and continuous-discrete settings as these systems have great applications in engineering fields such as process control, multi-dimensional digital filtering, image processing, see for instance [1–6].Among the most of the existed literature on filtering problems, the disturbances are considered in the entire frequency (EF) domain, which will bring over design in the filtering design
The main objective of this paper is to design a filter for discrete T-S fuzzy Fornasini-Marchesini Models with disturbance in finite frequency (FF) domain
Summary
In the last few decades, many researchers have investigated two-dimensional (2-D) systems including continuous, discrete and continuous-discrete settings as these systems have great applications in engineering fields such as process control, multi-dimensional digital filtering, image processing, see for instance [1–6]. Among the most of the existed literature on filtering problems, the disturbances are considered in the entire frequency (EF) domain, which will bring over design in the filtering design. While many practical engineering problems are more suitable to be considered in finite frequency (FF) ranges. The standard design approaches for the whole frequency domain may bring conservatism (see, [11–14] and the references therein). The main objective of this paper is to design a filter for discrete T-S fuzzy Fornasini-Marchesini Models with disturbance in FF domain. A systematic filter design scheme is proposed, which could reduce the conservatism of the results compared to the one considered in EF domain. Notations Superscript ”T ” stands for matrix transposition. Notation P > 0 means that matrix P is positive. I denotes an identity matrix with appropriate dimension. A 2D signal u(i, j) in the l2 space is an energy-bounded signal
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