This paper aims to investigate the problem of robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delay. Two new delay-dependent stability criteria for such systems are proposed. The first criterion is based on estimating the forward difference of Lyapunov–Krasovskii functional using a summation inequality along with the Wirtinger-based inequality. The second one employs the method of delay partitioning where the delay range is nonuniformly divided into subintervals. The proposed criteria are distinctive and may be considered less stringent than previous criteria. Examples are presented to verify the effectiveness of the criteria.
AgarwalNKarH (2014) An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow. Digital Signal Processing28: 136–143.
2.
BakuleLRodellarJRossellJM (2006) Robust overlapping guaranteed cost control of uncertain state-delay discrete-time systems. IEEE Transactions on Automatic Control51(12): 1943–1950.
3.
BoydSEl GhaouiLFeronE, et al. (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM.
4.
ButterweckHJRitzerfeldJHFWerterMJ (1988) Finite wordlength effects in digital filters: A review. EUT report 88-E-205. Eindhoven: Eindhoven University of Technology.
5.
ChangTL (1981) Suppression of limit cycles in digital filters designed with one magnitude-truncation quantizer. IEEE Transactions on Circuits and Systems28(2): 107–111.
6.
ChenWHGuanZHLuX (2003) Delay-dependent guaranteed cost control for uncertain discrete-time systems with delay. IEE Proceedings—Control Theory and Applications150(4): 412–416.
7.
ChenWHGuanZHLuX (2004) Delay-dependent guaranteed cost control for uncertain discrete-time systems with both state and input delays. Journal of the Franklin Institute341(5): 419–430.
8.
ClassenTACMMecklenbräukerWFGPeekJBH (1976) Effects of quantization and overflow in recursive digital filters. IEEE Transactions on Acoustics, Speech, and Signal Processing24(6): 517–529.
9.
EricksonKMichelA (1985) Stability analysis of fixed-point digital filters using computer generated Lyapunov functions-Part I: Direct form and coupled form filters. IEEE Transactions on Circuits and Systems32(2): 113–132.
10.
GahinetPNemirovskiiALaubAJ, et al. (1995) LMI Control Toolbox—For Use with Matlab. Natick, MA: MathWorks.
11.
GuanXLinZDuanG (1999) Robust guaranteed cost control for discrete-time uncertain systems with delay. IEE Proceedings—Control Theory and Applications146(6): 598–602.
12.
GuptaPKSinghKKandanvliVKR, et al. (2023) New criterion for the stability of discrete-time systems with state saturation and time-varying delay. Journal of Control, Automation and Electrical Systems34: 700–708.
13.
HeYWangQGXieL, et al. (2007) Further improvement of free-weighting matrices technique for systems with time-varying delay. IEEE Transactions on Automatic Control52(2): 293–299.
14.
HuJWangZGaoH, et al. (2011) Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonlinearities. IEEE Transactions on Industrial Electronics59(7): 3008–3015.
15.
JiangXHanQLYuX (2005) Stability criteria for linear discrete-time systems with interval-like time-varying delay. In: Proceedings of the 2005, American control conference, Portland OR, 8–10 June, pp. 2817–2822. New York: IEEE.
16.
KandanvliVKRKarH (2009) An LMI condition for robust stability of discrete-time state-delayed systems using quantization/overflow nonlinearities. Signal Processing89(11): 2092–2102.
17.
KandanvliVKRKarH (2011) Delay-dependent LMI condition for global asymptotic stability of discrete time uncertain state-delayed systems using quantization/overflow nonlinearities. International Journal of Robust and Nonlinear Control21(14): 1611–1622.
18.
KanithiSKMSinghKKandanvliVKR, et al. (2024) Discrete-time state delayed systems with saturation arithmetic: Overflow oscillation-free realization. Smart Science12(1): 43–52.
19.
KarH (2011) Asymptotic stability of fixed-point state-space digital filters with combinations of quantization and overflow nonlinearities. Signal Processing91(11): 2667–2670.
20.
LiNMaHDuC, et al. (2021) Distributed adaptive containment control for a class of discrete-time nonlinear multi-agent systems with uncertainties. International Journal of Control94(8): 2186–2199.
21.
LiberzonD (2003) Switching in Systems and Control. Boston MA: Birkhäuser.
22.
LiuDMichelAN (1992) Asymptotic stability of discrete-time systems with saturation nonlinearities with applications to digital filters. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications39(10): 798–807.
23.
LiuJZhangJ (2012) Note on stability of discrete-time time-varying delay systems. IET Control Theory and Applications6(2): 335–339.
24.
LöfbergJ (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD conference, Taipei, Taiwan, 2–4 September, pp. 284–289. New York: IEEE.
25.
MahmoudMS (2013) Stabilization of interconnected discrete systems with quantization and overflow nonlinearities. Circuits, Systems, and Signal Processing32(2): 905–917.
26.
MaryTJRangarajanP (2016) Delay-dependent stability analysis of microgrid with constant and time-varying communication delays. Electric Power Components and Systems44(13): 1441–1452.
27.
MengXLamJDuB, et al. (2010) A delay-partitioning approach to the stability analysis of discrete-time systems. Automatica46(3): 610–614.
28.
NamPTPathiranaPNTrinhH (2015) Discrete Wirtinger-based inequality and its application. Journal of the Franklin Institute352(5): 1893–1905.
29.
PandeySTadepalliSKBhusnurS, et al. (2024) Improved stability and passivity results for discrete time-delayed systems with saturation nonlinearities and external disturbances. Circuits, Systems, and Signal Processing43: 103–123.
30.
ParkPKoJWJeongC (2011) Reciprocally convex approach to stability of systems with time-varying delays. Automatica47(1): 235–238.
31.
SeuretAGouaisbautFFridmanE (2015) Stability of discrete-time systems with time-varying delays via a novel summation inequality. IEEE Transactions on Automatic Control60(10): 2740–2745.
32.
SinghKGuptaPKChaurasiaD, et al. (2022) Stability of discrete-time delayed systems subject to external interference and generalized overflow nonlinearities. IEEE Transactions on Industry Applications58(4): 5353–5364.
33.
SinghKKandanvliVKRKarH (2021) Delay partitioning approach to the robust stability of discrete-time systems with finite wordlength nonlinearities and time-varying delays. Transactions of the Institute of Measurement and Control43(4): 958–974.
34.
TadepalliSKKandanvliVKR (2016) Improved stability results for uncertain discrete-time state-delayed systems in the presence of nonlinearities. Transactions of the Institute of Measurement and Control38(1): 33–43.
35.
TadepalliSKKandanvliVKRVishwakarmaA (2018) Criteria for stability of uncertain discrete-time systems with time-varying delays and finite wordlength nonlinearities. Transactions of the Institute of Measurement and Control40(9): 2868–2880.
36.
TutsoyOPolatAÇolak BalikciŞK (2020) Development of a multi-dimensional parametric model with non-pharmacological policies for predicting the COVID-19 pandemic casualties. IEEE Access8: 225272–225283.
37.
WuZGParkJHSuH, et al. (2012) Robust dissipativity analysis of neural networks with time-varying delay and randomly occurring uncertainties. Nonlinear Dynamics69(3): 1323–1332.
38.
XuSLamJYangC (2001) Quadratic stability and stabilization of uncertain linear discrete-time systems with state delay. Systems & Control Letters43(2): 77–84.
39.
XueYLiHYangX (2018) An improved reciprocally convex inequality and application to stability analysis of time-delay systems based on delay partition approach. IEEE Access6: 40245–40252.
40.
XueYZhangXHanYY, et al. (2016) A delay-range-partition approach to analyse stability of linear systems with time-varying delays. International Journal of Systems Science47(16): 3970–3977.
41.
ZhangCKHeYJiangL, et al. (2016a) An improved summation inequality to discrete-time systems with time-varying delay. Automatica74: 10–15.
42.
ZhangJPengCZhengM (2016b) Improved results for linear discrete-time systems with an interval time-varying input delay. International Journal of Systems Science47(2): 492–499.
43.
ZouLWangZHanQL, et al. (2019) Moving horizon estimation for networked time-delay systems under Round-Robin protocol. IEEE Transactions on Automatic Control64(12): 5191–5198.
