Abstract
This paper deals with the problem ofH∞model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FFH∞model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposedH∞model reduction design, a numerical example is given.
Highlights
During the past decades, much progress has been made for 2D systems in the literature [1, 2], many important results based on Linear Matrix Inequalities (LMIs) approach have already been reported
Much progress has been made for 2D systems in the literature [1, 2], many important results based on LMI approach have already been reported
The point of interest in aforementioned literature is that all performance indices are defined in the entire frequency (EF) domain
Summary
Much progress has been made for 2D systems in the literature [1, 2], many important results based on LMI approach have already been reported. Among these results, stability analysis and stabilization design for 2D systems have been studied in [3], H∞ filtering problem can be found in [14], model reduction problem in [6]. Notations Superscript ”T ” stands for matrix transposition. Notation P > 0 means that matrix P is positive. A 2D signal u(i, j) in the l2 space is an energy-bounded signal
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