Optimal guaranteed cost control of uncertain 2D discrete systems with both shift delays and input delays via memory state feedback

Abstract

The problem of optimal guaranteed cost control for a class of 2D discrete uncertain systems under shift delays and input delays in a Fornasini–Marchesini (FM) second model setting via memory state feedback is considered in this paper. A linear matrix inequality (LMI)-based criterion for the existence of guaranteed cost controllers is established. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. Illustrative examples are given to demonstrate the applicability of the proposed method.

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

“…Lemma 1 (Paszke et al, 2004; Tiwari and Dhawan, 2013). The closed-loop system (4) is asymptotically stable, provided there exist n×n positive definite symmetric matrices P , Q , Q 1 , Q 2 , Q 3 , Q 4 , Q 5 , Q 6 and Q 7 such that…”

“…In the real world, the process dynamics of many physical systems are affected by delays. As the presence of delays is frequently a source of instability and poor performance of many control systems, the study of 2-D discrete systems with delays has attracted many researchers and useful results have been reported in the literature (Paszke et al, 2004; Peng et al, 2007; Tiwari and Dhawan, 2012a, 2012b, 2013; Xu and Yu, 2009a, 2009b; Xu et al, 2007; Ye et al, 2009). In Xu et al (2007), a sufficient condition for the stability of 2-D discrete state-delayed systems in the general model (GM) has been derived via the Lyapunov approach.…”

“…A solution to the guaranteed cost control problem via memory state feedback control laws for a class of uncertain 2-D discrete state-delayed systems described by the FM second model was presented in Tiwari and Dhawan (2012b). In Tiwari and Dhawan (2013), the problem of optimal guaranteed cost control for a class of uncertain 2-D discrete systems described by the FM second model with both state and input delays via memory state feedback was considered. The problem of delay–dependent guaranteed cost control via memoryless state feedback for uncertain 2-D discrete state-delayed systems described by the FM second model was studied in Xu and Yu (2009a).…”

Design of Optimal Hybrid Controller for Multi-Phase Batch Processes With Interval Time Varying Delay

“…Hao et al [38] proposed an iterative learning control method for batch processes with input delay and uncertainties. Tiwari et al [39] designed an optimal guaranteed cost control of uncertain 2D discrete systems with both shift delays and input delays via memory state feedback. The time delay reflected in the system input is called the input time delay, and if reflected in the system state, it is called the state time delay.…”

“…Its main idea is to guarantee robust stability and make the worsening performance indicators resulting from system uncertainty still lower than some certain upper bound. In order to meet demands in actual production and obtain better high-precision control of system, studies have been extended to 2D systems and extensively applied in all areas [31], [39], [47]- [52]. Wang et al [31] presented the optimal designed algorithm of 2D hybrid robust iterative learning fault-tolerant guaranteed control.…”