Approach to delay‐dependent robust stability and stabilisation of delta operator systems with time‐varying delays

Aiss, Hicham El; Rachid, Hafsaa; Hmamed, Abdelaziz

doi:10.1049/iet-cta.2017.0006

Cited by 14 publications

(10 citation statements)

References 29 publications

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“…The work in [25,26] used a single-term approximation, and two-delay-term approximation was used in [27]. In [6,11], three delay terms were used, and it was shown that the three-delay-term approximation leads to less conservative results than one and two terms. Here, we use the three-term approximation, so we express ξ(t k − r h ) as follows:…”

Section: New Model Reformulationmentioning

confidence: 99%

“…Concerning the approximation error, we will use the same steps of the work [11]. Before moving on, the following lemma guarantees that the l 2 induced norm of ∆ is bounded by one.…”

Section: New Model Reformulationmentioning

confidence: 99%

“…In Reference [10], the authors used the delta operator approach to investigates the robust H ∞ filtering design for T-Sfuzzy systems with uncertainties and time-varying delay. In Reference [11], the robust stability of delta operator systems was discussed via the three-term approximation approach.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

2019

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The design of an anti-windup controller for delta operator systems with time-varying delay and actuator saturation is addressed. By utilizing the input-output approach and three-term approximation, we first transform the original system into two equivalent interconnected subsystems. Then, by employing the scaled small-gain theorem, the Lyapunov–Krasovskii functional, and Wirtinger’s integral inequality, sufficient conditions for the synthesis of an anti-windup compensator are presented in the form of linear matrix inequalities (LMIs). The estimated domain of attraction is maximized by an optimization algorithm. Numerical examples are studied to show the merits of the proposed technique.

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Section: New Model Reformulationmentioning

confidence: 99%

“…Concerning the approximation error, we will use the same steps of the work [11]. Before moving on, the following lemma guarantees that the l 2 induced norm of ∆ is bounded by one.…”

Section: New Model Reformulationmentioning

confidence: 99%

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Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

2019

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“…The obtained maximum allowable upper bound can be considered as an important index to evaluate the conservatism of the stability criterion. In order to derive a less conservative stability criterion, several methods are utilized, such as transformation technique, free weighting matrices technique, integral/summation inequalities method, delay‐partitioning method, and input‐output approach combined with scaled small gain theorem …”

Section: Introductionmentioning

confidence: 99%

“…In order to derive a less conservative stability criterion, several methods are utilized, such as transformation technique, 16 free weighting matrices technique, 17 integral/summation inequalities method, 18 delay-partitioning method, 19 and input-output approach combined with scaled small gain theorem. 20,21 In the past few years, many works have focused on the study of to the problem of delay-dependent stability for 2D systems with delays, to mention a few: in the work of Yao et al, 22 the free-weighting matrices has been introduced to cope with the stability analysis of 2D state-delayed systems described by the FM second model. In the work of Hien and Trinh, 23 new 2D finite-sum inequalities have been proposed to deal with the problem of stability analysis of discrete-time 2D Roesser systems with interval time-varying delays.…”

Section: Introductionmentioning

confidence: 99%

Exponential stability analysis for 2D discrete switched systems with state delays

Badie

Alfidi

Chalh

2019

Optim Control Appl Methods

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Summary This paper is concerned with the delay‐dependent exponential stability analysis of two‐dimensional (2D) discrete switched systems with state delays described by the Roesser model; the delays under consideration are varying. By constructing an appropriate Lyapunov‐Krasovskii functional and using the average dwell time approach, new delay‐dependent sufficient conditions for the exponential stability of the system under study are proposed. In order to obtain less conservative conditions, the delay partitioning method is adopted as well as the free‐weighting matrix technique. The proposed conditions are formulated in the format of linear matrix inequality. The effectiveness and the reduced conservatism of the developed results are shown by illustrative examples.

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Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

Charqi

Tissir

Boukili

2020

Optim Control Appl Methods

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Summary This article deals with the problems of stability and stabilization for a class of discrete‐time switched systems with time‐varying delay under arbitrary switching signal. First, sufficient conditions guaranteeing the asymptotic stability of the unforced system are developed, by using the switched Lyapunov‐Krasovskii functional method. Then, based on the obtained results, a state feedback controller is designed in order to ensure the asymptotic stability of the closed‐loop system. Furthermore, slack variables are introduced for more relaxation. The proposed approach is proved to have some less conservative results than some existing works. Finally, numerical examples are provided to illustrate the effectiveness and the merit of the proposed method and to compare the obtained results with some previous works in the literature.

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Approach to delay‐dependent robust stability and stabilisation of delta operator systems with time‐varying delays

Cited by 14 publications

References 29 publications

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

Stabilization of Delta Operator Systems with Actuator Saturation via an Anti-Windup Compensator

Exponential stability analysis for 2D discrete switched systems with state delays

Asymptotic stability and stabilization of discrete‐time switched systems with time‐varying delay

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