An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

Tiwari, Manish; Dhawan, Amit

doi:10.1007/s00034-012-9410-5

Cited by 9 publications

(5 citation statements)

References 23 publications

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“…(2009) were corrected in Tiwari and Dhawan (2012b). 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 has been presented in Tiwari and Dhawan (2012c) and it has been shown with the help of illustrative examples that the criterion given in Tiwari and Dhawan (2012c) provides less conservative results than the approach given in Ye et. al.…”

Section: Introductionmentioning

confidence: 99%

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

Tandon

Dhawan

Tiwari

2018

Transactions of the Institute of Measurement and Control

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This paper is concerned with the problem of optimal guaranteed cost control via memory state feedback for a class of uncertain two-dimensional (2-D) discrete state-delayed systems described by the Roesser model with norm-bounded uncertainties. A linear matrix inequality (LMI)-based sufficient condition for the existence of memory state feedback guaranteed cost controllers is established and a parameterized representation of such controllers (if they exist) is given in terms of feasible solutions to a certain LMI. Furthermore, a convex optimization problem with LMI constraints is formulated to select the optimal guaranteed cost controllers that minimize the upper bound of the closed-loop cost function. The proposed method yields better results in terms of least upper bound of the closed-loop cost function as compared with a previously reported result.

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Section: Introductionmentioning

confidence: 99%

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

Tandon

Dhawan

Tiwari

2018

Transactions of the Institute of Measurement and Control

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“…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.…”

Section: Introductionmentioning

confidence: 99%

“…In Tiwari and Dhawan (2012a), several technical errors that have occurred in the main results of Ye et al (2009) were pointed out and corrected. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Tandon

Dhawan

2016

Transactions of the Institute of Measurement and Control

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In this paper, we present a solution to the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional(2-D) discrete systems described by the general model (GM) subject to both state and input delays. The parameter uncertainties are assumed norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of non-fragile robust guaranteed cost controller is established. Furthermore, a convex optimization problem with LMI constraints is proposed to select a non-fragile robust optimal guaranteed cost controller stabilizing the uncertain 2-D discrete system with both state and input delays as well as achieving the least guaranteed cost for the resulting closed-loop system. The effectiveness of the proposed method is demonstrated with an illustrative example.

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“…Several technical errors that have occurred in the main results of [35] were corrected in [30]. A solution to the guaranteed cost control A. K. Singh et al problem via memory state feedback control laws for a class of uncertain 2-D discrete state-delayed systems described by the FM second model has been presented in [31].…”

Section: Introductionmentioning

confidence: 99%

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

Singh¹,

Tandon²,

Dhawan³

2016

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This paper considers the problem of delay-dependent robust optimal H ∞ control for a class of uncertain two-dimensional (2-D) discrete state delay systems described by the general model (GM). The parameter uncertainties are assumed to be normbounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of delay-dependent γ-suboptimal state feedback robust H ∞ controllers which guarantees not only the asymptotic stability of the closed-loop system, but also the H ∞ noise attenuation γ over all admissible parameter uncertainties is established.Furthermore, a convex optimization problem is formulated to design a delay-dependent state feedback robust optimal H ∞ controller which minimizes the H ∞ noise attenuation γ of the closed-loop system. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed method.

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An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

Cited by 9 publications

References 23 publications

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

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

Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

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An LMI Approach to Optimal Guaranteed Cost Control of Uncertain 2-D Discrete Shift-Delayed Systems via Memory State Feedback

Cited by 9 publications

References 23 publications

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

Optimal guaranteed cost control of uncertain 2-D discrete state-delayed systems described by the Roesser model via memory state feedback

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

Delay-Dependent Robust &lt;i&gt;H&lt;/i&gt;&lt;sub&gt;∞&lt;/sub&gt; Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model

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Delay-Dependent Robust <i>H</i><sub>∞</sub> Control for Uncertain 2-D Discrete State Delay Systems Described by the General Model