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 (https://dx-doi-org.web.bisu.edu.cn/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.

Keywords

2-D discrete systems guaranteed cost control linear matrix inequality Lyapunov methods robust stability state-delayed systems uncertain systems

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