Non-Fragile Robust Guaranteed Cost Control of 2-D Discrete Uncertain Systems Described by the General Models

Abstract

The problem of non-fragile robust guaranteed cost control for a class of two-dimensional (2-D) discrete systems in the general model (GM) with norm-bound uncertainties is investigated. The purpose is to design a non-fragile state feedback controller such that the closed-loop system is asymptotically stable and the cost function value is not more than an upper bound for all admissible uncertainties. The cost function is proposed and an upper bound of the cost function is given. By using a linear matrix inequalities (LMIs) approach, a sufficient condition for the solvability of the problem is obtained. A desired non-fragile state feedback controller can be constructed by solving a set of LMIs. An example is provided to demonstrate the application of the proposed design method.

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’

“…During the past two decades, the guaranteed cost control problem for a two-dimensional (2-D) discrete system has drawn the attention of many researchers (see Dhawan and Kar, 2007, 2011; Hien and Trinh, 2017; Tandon and Dhawan, 2016; Xu and Yu, 2009; Ye et al, 2011, and the references cited therein for a sample of the literature) due to its extensive application in controlling a real plant. The aim of guaranteed cost control is to design a controller such that the resulting closed-loop system is asymptotically stable and an upper bound on the closed-loop cost function is guaranteed.…”

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

“…Recently, research on non-fragile control problem has attracted attention (Dhawan, 2012; Sharma and Dhawan, 2012; Tandon and Dhawan, 2014, 2016; Ye et al, 2011). The objective of non-fragile control is to design a controller for a given system such that the controller is insensitive to some amount of error with respect to its gain, i.e.…”

“…the controller is non-fragile (Yang and Wang, 2001). In Ye et al (2011), the problem of non-fragile robust guaranteed cost control for a class of uncertain 2-D discrete systems described by the GM has been considered and a sufficient condition for the existence of non-fragile robust guaranteed cost controllers has been established via a linear matrix inequality (LMI) approach. A solution to the non-fragile robust optimal guaranteed cost control problem for a class of 2-D discrete systems described by the GM has been presented in Tandon and Dhawan (2014) and it has been shown that their approach provides less stringent results than that given in Ye et al (2011).…”

“…In Ye et al (2011), the problem of non-fragile robust guaranteed cost control for a class of uncertain 2-D discrete systems described by the GM has been considered and a sufficient condition for the existence of non-fragile robust guaranteed cost controllers has been established via a linear matrix inequality (LMI) approach. A solution to the non-fragile robust optimal guaranteed cost control problem for a class of 2-D discrete systems described by the GM has been presented in Tandon and Dhawan (2014) and it has been shown that their approach provides less stringent results than that given in Ye et al (2011). Very recently, the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain 2-D discrete state-delayed systems described by the GM has been studied in Tandon and Dhawan (2016) and it has also been shown that the proposed method leads to a tighter upper bound of the closed-loop cost function compared with that obtained in Tandon and Dhawan (2014).…”

An LMI approach to non-fragile robust optimal guaranteed cost control of 2D discrete uncertain systems

“…Since controller fragility is basically the performance deterioration of a feedback control system due to inaccuracies in controller implementation, the non-fragile control problem for one-dimensional (1D) and 2D systems has been investigated in Dhawan (2012); Haddad and Corrado (2000); Lien (2007aLien ( , 2007b; Park (2004); Sharma and Dhawan (2012); Wu et al (2012); Xu et al (2009); and Yang and Wang (2001). Recently, the non-fragile robust guaranteed cost control problem for a class of 2D discrete systems described by the GM (Kurek, 1985) has been studied in Ye et al (2011) and a linear matrix inequality (LMI)-based sufficient condition for the existence of a non-fragile robust guaranteed cost controller has been presented. However, the approach of Ye et al (2011) is not suitable for the design of non-fragile robust optimal guaranteed cost controller that renders the corresponding guaranteed cost as small as possible.…”