Comments on ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’

Abstract

This paper points out some technical errors in a recent paper that appeared in Transactions of the Institute of Measurement and Control entitled ‘An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays’ by Akshata Tandon and Amit Dhawan ( http://dx.doi.org/10.1177/0142331216667476 ). We reveal that the upper bound of the closed-loop cost function provided by their Lemma 4 is erroneous. Some critical issues associated with the system initial conditions assumed in their paper are highlighted. The closed-loop cost bound claimed by their Theorem 1 is found to be incorrect. The optimization problem formulated in their Theorem 2 for the selection of an optimal guaranteed cost controller is erroneous. Finally, the corrections over their results are made available.

H∞ control for a class of two-dimensional linear systems with fading measurements

“…Two-dimensional (2-D) systems have been widely and successfully applied in numerous important processes in practice such as linear image processing, digital filtering, gas absorption, and so on (Ahn et al, 2015; Du and Xie, 2002; Du et al, 2001; Duan and Xiang, 2014; Efe, 2006). In the past few years, many significant techniques and methods have been developed to study the synthesis and analysis of 2-D systems, including stabilization and performance problems (Agarwal and Kar, 2018a; Chang et al, 2015, 2019; Chen, 2010; Kaczorek, 1996; Liu, 2015), filtering problems (Du et al, 2000), guaranteed cost control problems (Agarwal and Kar, 2018b; Tandon and Dhawan, 2014, 2018), and so forth.…”