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

Abstract

This paper addresses the problem of non-fragile robust optimal guaranteed cost control for a class of two-dimensional discrete systems described by the general model with norm-bounded uncertainties. Based on Lyapunov method, a new linear matrix inequality (LMI)-based criterion for the existence of non-fragile state feedback controller is established. Furthermore, a convex optimization problem with LMI constraints is formulated to select a non-fragile robust optimal guaranteed cost controller, which minimizes the upper bound of the closed-loop cost function. The merit of the proposed criterion in aspect of conservativeness over a recently reported criterion is demonstrated with the help of illustrative examples.

Robust nonfragile observer-based H2/H∞ controller

“…An ultimate goal of the robust nonfragile control system is to analyze the effects of the implementation imperfections by means of evaluating the effectiveness of the control system on the full order system (see Figure 2). A large body part of the literature in this area has developed based on continuous state space representation which is not applicable in practice (except for Che and Yang, 2008; Hsieh et al., 2005; Kchaou et al., 2012; Tandon and Dhawan, 2014; Yee et al. 2001; Zhang et al., 2012, 2014, 2015).…”

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.…”

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.…”

“…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).…”

“…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). It may be mentioned here that all the results reported so far in the literature for the non-fragile robust guaranteed cost control problem for uncertain 2-D discrete systems consider only state delays, whereas in many real situations, input delays are often encountered because of transmission of the measurement information.…”