Delay-dependent state feedback stabilization for a networked control model with two additive input delays

Shao, Hanyong; Zhang, Zhengqiang

doi:10.1016/j.amc.2015.05.114

Cited by 34 publications

(12 citation statements)

References 25 publications

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“…The system with time delays commonly includes one single delay. However, for some real world systems such as networked control systems [26], [27], the delays may be induced from the different channels. For example, as in Figure 1, there can be two separate delays: one is from sensor to controller, and the other is from controller to actuator.…”

Section: Introductionmentioning

confidence: 99%

“…In [30], [31], to improve conservatism of the stability condition, the relationship between the timevarying delay and its upper bound was further considered in the process of estimating the derivative of LKF. Besides, many researchers have tried to achieve a MUBTD guaranteeing asymptotic stability [26], [32], [33], [34], [35]. More recently, the authors of [36] tried to take into account more information of system with ATDs by introducing an improved delay interconnection integral terms.…”

Section: Introductionmentioning

confidence: 99%

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New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

2020

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This paper is concerned with the problem of stability analysis for systems with additive time-varying delays (ATDs). This paper proposes a new free-matrix-based integral inequality that provides estimate of the energy of the vector that contains the state and its derivative at the same time. Consequently, the proposed inequality enables the Lyapunov-Krasovskii functional (LKF) to take into account not only the respective energies of the state and its derivatives but also the correlated effect of them. Then, based on the proposed inequality, this paper derives a new stability criterion of systems with ATDs. This paper constructs LKF by proposing new sets of multiple subintervals of the ATDs, and makes use of the proposed inequality when estimating the derivatives of the LKF. This allows the resulting stability criterion to take full advantage of the information of the multiple subintervals of the ATDs. This paper also successfully applies the proposed free-matrix-based integral inequality to the system with a single time-varying delay. Three numerical examples demonstrate the effectiveness of the proposed methods.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

2020

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“…Since the distribution characteristic of delays mentioned above has been modeled firstly as a system with two additive time-varying delay components in [4], many significant results have been devoted to this issue. As a most general form, linear systems with two additive delay components have drawn lots of attention [5][6][7][8][9][10][11][12][13][14][15]. Moreover, neural networks [16][17][18][19][20][21], T-S fuzzy systems [22,23], and Lur'e systems [24], considering two additive delay components in the state, have been also investigated recently.…”

Section: Introductionmentioning

confidence: 99%

“…Some criteria with less conservatism are obtained in [8] by taking the delay, its upper bound, and the relationship between them into account. A novel LKF [9] is constructed, for which positive definiteness is ensured by the whole LKF rather than each term. In [10], a delay-partitioningbased LKF was established, which greatly reduces the conservatism.…”

Section: Introductionmentioning

confidence: 99%

New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Liu

2020

Complexity

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This paper focuses on the stability problems of continuous linear systems with two additive time-varying delay components. Firstly, an effective and simple Lyapunov–Krasovskii functional (LKF) is established, which not only takes adequate information of delay components and their upper bounds into consideration but also establishes a simpler form to decrease the computational complexity. Secondly, an improved delay-dependent stability criterion together with its corollary is obtained by employing the generalized free-weighting-matrix-based (GFWM-based) inequality and some other techniques to calculate the derivative of the constructed LKF, which will further reduce the introduced estimation error and make the criteria less conservative. Lastly, a numerical example is presented to illustrate the less conservatism and lower computational complexity of the derived results.

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“…In general, stability analysis of time-delay systems is classified into two categories such as delay-independent and delay-dependent stability criterion in which the later one uses the information of maximal delay bound and the former one does not. Delay-dependent case has the advantage of using information on the maximal size of the delay bound [10][11][12], and hence, it yields less conservative result over the delay-independent case [13]. For the recent progress of time-delay system, the reader may refer to [14][15][16][17][18][19][20][21] and the reference therein.…”

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confidence: 99%

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

Sakthivel

Selvaraj

et al. 2017

Intl J Robust & Nonlinear

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Summary This paper addresses the passivity‐based H∞ control problem for a class of time‐varying delay systems subject to nonlinear actuator faults and randomly occurring uncertainties via fault‐tolerant controller. More precisely, the uncertainties are described in terms of stochastic variables, which satisfies Bernoulli distribution, and the existence of actuator faults are assumed not only linear but also nonlinear, which is a more general one. The main objective of this paper is to design a state feedback‐reliable controller such that the resulting closed‐loop time‐delay system is stochastically stable under a prescribed mixed H∞ and passivity performance level γ>0 in the presence of all admissible uncertainties and actuator faults. Based on Lyapunov stability method and some integral inequality techniques, a new set of sufficient conditions is obtained in terms of linear matrix inequality (LMI) constraints to ensure the asymptotic stability of the considered system. Moreover, the control design parameters can be computed by solving a set of LMI constraints. Finally, two examples including a quarter‐car model are provided to show the efficiency and usefulness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd.

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Delay-dependent state feedback stabilization for a networked control model with two additive input delays

Cited by 34 publications

References 25 publications

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

New Free-Matrix-Based Integral Inequality: Application to Stability Analysis of Systems With Additive Time-Varying Delays

New Stability Analysis Results for Linear System with Two Additive Time-Varying Delay Components

Delay‐dependent fault‐tolerant controller for time‐delay systems with randomly occurring uncertainties

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