Enhanced Stability Criteria for Discrete-time Systems with Time-varying Delay

다국어 초록 (Multilingual Abstract)

The stability problem of discrete-time linear systems with interval time-varying delays is investigated in this paper. According to the latest summation inequality technique, an improved free-matrix-based summation inequality is proposed in this paper. In order to make full use of the improved inequality to bound the upper bounds of the difference Lyapunov-Krasovskii functional (LKF), an augmented LKF with some extra status information is constructed. A new delay-range-dependent stability criterion is derived in the form of linear matrix inequalities (LMIs) via the modified LKF approach. The criterion is less conservative than some existing results. Finally, some standard numerical examples are presented the effectiveness of the proposed approach.

참고문헌 (Reference)

1 J. Chen, "Summation innequality and its application to stability analysis for time-delay systems" 10 : 391-395, 2016

2 A. Seuret, "Stability of linear systems with time-varying delays using Bessel-Legendre inequalities" 63 (63): 225-232, 2018

3 A. Seuret, "Stability of discrete-time systems with time-varying delays via a novel summation inequality" 60 : 2740-2745, 2015

4 O. Kwon, "Stability and stabilization for discrete-time systems with time-varying delays via augmented Lyapunov-Krasovskii functional" 350 : 521-540, 2013

5 P. Park, "Stability and robust stability for systems with a time-varying delay" 43 (43): 1855-1858, 2007

6 S. Qiu, "Stability and passivity analysis of discrete-time linear systems with time-varying delay" 134 : 104543-, 2019

7 W. Chen, "Stability analysis of neutral systems with mixed interval time-varying delays and nonlinear disturbances" 357 (357): 3721-3740, 2020

8 H. Zeng, "Stability analysis of generalized neural networks with time-varying delays via a new integral inequality" 161 : 148-154, 2015

9 J. Chen, "Stability analysis of discretetime neural networks with an interval-like time-varying delay" 329 : 248-254, 2019

10 E. Tian, "Robust H∞ control for nonlinear systems over network : A piecewise analysis method" 161 (161): 2731-2745, 2010

11 X. Zhang, "Overview of recent advances in stability of linear systems with time-varying delays" 13 : 1-16, 2018

12 Y. He, "Output feedback stabilization for a discrete-time system with a time-varying delay" 53 : 2372-2377, 2008

13 H. Zhang, "Novel synchronization conditions for time-varying delayed Lur’e system with parametric uncertainty" 350 : 224-236, 2019

14 X. Zhang, "Novel stability criteria for linear time-delay systems using Lyapunov-Krasovskii functionals with a cubic polynomial on time-varying delay" 8 (8): 77-85, 2021

15 C. Zhang, "Notes on stability of time-delay systems : Bounding inequalities and augmented lyapunov-krasovskii functionals" 62 : 5331-5336, 2017

16 J. Liu, "Note on stability of discrete-time time-varying delay systems" 6 : 335-339, 2012

17 D. Liao, "New stability criteria of discrete systems with time-varying delays" 7 : 1677-1684, 2019

18 H. Shao, "New stability criteria for linear discrete-time systems with interval-like time-varying delays" 56 : 619-625, 2011

19 W. Duan, "New results on stability analysis of uncertain neutral-type Lur’e systems derived from a modified Lyapunov-Krasovskii functional" 2019 : 2019

20 J. Yogambigai, "Impulsive and pinning control synchronization of Markovian jumping complex dynamical networks with hybrid coupling and additive interval time-varying delays" 85 : 105-215, 2020

21 B. Zhang, "Improved stability criterion and its applications in delayed controller design for discrete-time systems" 44 (44): 2963-2967, 2008

22 Z. Gao, "Improved stability criteria for the neural networks with time-varying delay via new augmented Lyapunov-Krasovskii functional" 349 : 258-269, 2019

23 J. Zhang, "Improved results for linear discrete-time systems with an interval time-varying input delay" 47 : 492-499, 2016

24 Wen-Yong Duan, "Improved Sufficient LMI Conditions for the Robust Stability of Timedelayed Neutral-type Lur’e Systems" 제어·로봇·시스템학회 16 (16): 2343-2353, 2018

25 Shen-Ping Xiao, "Improved Stability Criteria for Discrete-time Delay Systems via Novel Summation Inequalities" 제어·로봇·시스템학회 16 (16): 1592-1602, 2018

26 X. Zhang, "Hierarchical type stability criteria for delayed neural networks via canonical Bessel-Legendre inequalities" 48 : 1660-1672, 2018

27 X. Zhang, "Global asymptotic stability for delayed neural networks using an integral inequality based on nonorthogonal polynomials" 29 : 4487-4493, 2018

28 B. Wang, "Fuzzy modelbased nonfragile control of switched discrete-time systems" 93 : 2461-2471, 2018

29 W. Duan, "Further stability analysis for time-delayed neural networks based on an augmented Lyapunov functional" 7 : 104655-104666, 2019

30 E. Suntonsinsoungvon, "Exponential stability of discrete-time uncertain neural networks with multiple time-varying leakage delays" 171 : 233-245, 2020

31 H. Lian, "Dissipativity analysis for neural networks with time-varying delays via a delay-product-type Lyapunov functional approach" 32 (32): 975-984, 2020

32 D. Gong, "Discrete legendre polynomials-based inequality for stability of timevarying delayed systems" 356 : 9907-9927, 2019

33 P. Nam, "Discrete inequalities based on multiple auxiliary functions and their applications to stability analysis of time-delay systems" 352 : 5810-5831, 2015

34 P. Nam, "Discrete Wirtingerbased inequality and its application" 352 : 1893-1905, 2015

35 C. Zhang, "Delaydependent stability analysis of neural networks with timevarying delay : A generalized free-weighting-matrix approach" 294 : 102-120, 2017

36 W. Duan, "Delay-range-dependent stability criteria for delayed discrete-time Lur’e system with sectorbounded nonlinearities" 78 (78): 135-145, 2014

37 C. Briat, "Convergence and equivalence results for the jensen’s inequality-Application to time-delay and sampleddata systems" 56 : 1660-1665, 2011

38 C. Briat, "Control and Observation of LPV Time-delay Systems" Grenoble-INP

39 S. Lee, "Bessel summation inequalities for stability analysis of discrete-time systems with timevarying delays" 29 : 473-491, 2019

40 C. Zhang, "An improved summation inequality to discrete-time systems with timevarying delay" 74 : 10-15, 2016

41 W. Duan, "An enhanced stability criterion for linear time-delayed systems via new LyapunovKrasovskii functionals" 2020 : 1-13, 2020

42 X. Zhang, "Abel lemma-based finite-sum inequality and its application to stability analysis for linear discrete time-delay systems" 57 : 199-202, 2015

43 D. Yue, "A piecewise analysis method to stability analysis of linear continuous/discrete systems with time-varying delay" 19 (19): 1493-1518, 2009

44 D. Liao, "A new result on stability analysis for discrete system with interval time-varying delays" 123 : 1-12, 2019

45 M. Obaiah, "A delay-dependent antiwindup compensator for wide-area power systems with time-varying delays and actuator saturation" 7 : 106-117, 2020