A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

Peng, Dan; Zhang, Jing; Chen, Hua; Gao, Chang

doi:10.1007/s12555-016-0518-4

Cited by 13 publications

(16 citation statements)

References 23 publications

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“…wherē In this example, the 2-D delta operator system (32) with 1 < d 1 (t j ) < 24 is asymptotically stable. However, systems in [2,10], and [12] are asymptotically stable for 1 < d 1 (t j ) < 13, 1 < d 1 (t j ) < 20, and 1 < d 1 (t j ) < 20, respectively. Time-delay upper bounds d 1M given in [2,10,12], and Theorem 1 in this paper are compared in Table 1.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…However, systems in [2,10], and [12] are asymptotically stable for 1 < d 1 (t j ) < 13, 1 < d 1 (t j ) < 20, and 1 < d 1 (t j ) < 20, respectively. Time-delay upper bounds d 1M given in [2,10,12], and Theorem 1 in this paper are compared in Table 1. Obviously, the time-delay upper bound d 1M provided in this paper is larger than the ones obtained in [2,10], and [12].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Time-delay upper bounds d 1M given in [2,10,12], and Theorem 1 in this paper are compared in Table 1. Obviously, the time-delay upper bound d 1M provided in this paper is larger than the ones obtained in [2,10], and [12].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Based on [10], an improved approach has been given in [11]. Besides, a delay-partitioning approach has been proposed in [12]. Most of the studies are mainly on 2-D discrete-time systems.…”

Section: Introductionmentioning

confidence: 99%

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Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

2018

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In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An estimate of the domain of attraction for the two-dimensional delta operator system is introduced to analyze stability of the closed-loop system. A state feedback controller is designed via a Lyapunov-Krasovskii functional approach for the two-dimensional delta operator system with time-varying delays and actuator saturation. Two numerical examples are given to illustrate the effectiveness and advantages of the developed techniques.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

“…Based on [10], an improved approach has been given in [11]. Besides, a delay-partitioning approach has been proposed in [12]. Most of the studies are mainly on 2-D discrete-time systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

2018

Self Cite

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“…Different from one-dimensional (1-D) systems, 2-D systems are a class of dynamic systems in which the information propagates along two independent directions, which make the study of those systems more complicated. However, many publications relating to the analysis and synthesis for 2-D systems have appeared; for example, the stability analysis problem for 2-D systems has been considered in Ahn et al (2016), Peng et al (2018) and Badie et al (2018a,b), and the control and filtering problems have been investigated in Xu and Zou (2010), Li and Gao (2013), Ghous and Xiang (2016) and Badie et al (2019a).…”

Section: Introductionmentioning

confidence: 99%

H_∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

Badie

Alfidi

Chalh

2020

Transactions of the Institute of Measurement and Control

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This paper is concerned with the H∞ filtering problem for two-dimensional (2-D) discrete switched systems described by the second Fornasini and Marchesini (FM) model. The main purpose is to design a switched filter such that the resulting filtering error system under the arbitrary switching signal is asymptotically stable with a guaranteed H∞ performance level. By using the switched Lyapunov functions, a new sufficient condition is obtained to guarantee the asymptotic stability with a H∞ performance index for the filtering error system. Based on this condition, the full- and reduced-order H∞ filter design conditions are derived and formulated in terms of linear matrix inequalities (LMIs). Two illustrative examples are utilized to show the effectiveness and less conservativeness of the proposed method.

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Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

Peng

Nie

2020

Asian Journal of Control

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The problem of delay‐dependent stability is concerned for two‐dimensional discrete‐time systems with interval time‐varying delays in this paper. Choosing a Lyapunov functional with the upper bound and lower bound of delays, considering all terms in the difference and using two‐dimensional Abel lemma‐based finite‐sum inequalities, a new delay‐dependent stability criterion in terms of linear matrix inequality is derived for two‐dimensional discrete‐time systems. Then, based on the delay‐dependent stability criteria, a state feedback control problem and a dynamic output feedback control problem are considered to realize the stability control for the two‐dimensional discrete‐time system. Finally, it is shown through four numerical examples that the stability criterion can provide a larger admissible maximum upper bound with less decision variables than the stability criterion using two‐dimensional Jensen inequalities approach.

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A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

Cited by 13 publications

References 23 publications

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

H_∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

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A Delay-partitioning Approach to the Stability Analysis of 2-D Linear Discrete-time Systems with Interval Time-varying Delays

Cited by 13 publications

References 23 publications

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

H∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model

Abel lemma‐based finite‐sum inequality approach to stabilization for 2‐D time‐varying delay systems

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H_∞ Filtering for two-dimensional discrete switched systems in the second Fornasini and Marchesini model