This paper presents a sufficient condition for exponential stability and confirms performance of state-delayed digital filters in the simultaneous existence of saturation arithmetic and external disturbance. The realization of limit-cycle free state-space digital filters is carried out by utilizing better characterization of saturation nonlinearities. The presented criterion not only ensures exponential stability but also reduces effect of external interference to a specific attenuation level. The obtained condition is in linear matrix inequality framework, so it is easily tractable. It is also shown that many results reported in literature may be retrieved as a special case from the proposed condition. With the help of numerical examples, it is shown that the presented approach provides enhanced stability region for the digital filters as compared to an existing criterion appeared in literature.
AfshariMMobayenSHajmohammadiRBaleanuD (2018) Global sliding mode control via LMI approach for uncertain chaotic systems with input nonlinearities and multiple delays. Journal of Computational and Nonlinear Dynamics13(3): 737–744.
2.
AhnCK (2011) Criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance. AEÜ - International Journal of Electronics and Communications65(9): 750–752.
3.
AmjadMURehanMTufailMet al. (2017) Stability analysis of nonlinear digital systems under hardware overflow constraint for dealing with finite word-length effects of digital technologies. Signal Processing140: 139–148.
4.
AntoniouA (2006) Digital Signal Processing. New York, NY, USA: Tata McGraw-Hill.
5.
ArifIRehanMTufailM (2017) Toward local stability analysis of externally interfered digital filters under overflow nonlinearity. IEEE Transactions on Circuits and Systems II: Express Briefs64(5): 595–599.
6.
BhargavaB (2001) A study of communication delays for web transactions. Cluster Computing4(4): 319–333.
7.
BoydSGhaouiLEFeronEBalakrishnanV (1994) Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM.
8.
ButterweckHJRitzerfeldJHFWerterMJ (1988) Finite wordlength effects in digital filters-a review. EUT Report 88-E-205, Eindhoven University of Technology, Eindhoven, The Netherlands.
9.
ChenS (2009) Asymptotic stability of discrete-time systems with time-varying delay subject to saturation nonlinearities. Chaos, Solitons & Fractals42(2): 1251–1257.
10.
ChoWChoiE (2017) A basis of spatial big data analysis with map-matching system. Cluster Computing20(3): 2177–2192.
11.
DengHDoroslovackiM (2006) Proportionate adaptive algorithms for network echo cancellation. IEEE Transactions on Signal Processing54(5): 1794–1803.
12.
Diksha, KokilPKarH (2016) Criterion for the limit cycle free state-space digital filters with external disturbances and quantization/overflow nonlinearities. Engineering Computations33(1): 64–73.
13.
ElaydiS (2005) An Introduction to Difference Equations. New York, USA: Springer.
14.
GahinetPNemirovskiALaubAJChilaliM (1995) LMI Control Toolbox. MA, USA: Mathworks Inc.
15.
GuKHanQLuoACJNiculescuS (2001) Discretized Lyapunov functional for systems with distributed delay and piecewise constant coefficients. International Journal of Control74(7): 737–744.
16.
HienLVTrinhH (2018) Exponential stability of two-dimensional homogeneous monotone systems with bounded directional delays. IEEE Transactions on Automatic Control63(8): 2694–2700.
17.
HilhorstGPipeleersGMichielsWSweversJ (2015) Sufficient LMI conditions for reduced-order multi-objective control of LTI systems. European Journal of Control23: 17–25.
18.
HongYLianY (2015) A memristor-based continuous-time digital FIR filter for biomedical signal processing. Transactions on Circuits and Systems I: Regular Papers62(5): 1392–1401.
19.
KandanvliVKRKarH (2008) Robust stability of discrete-time state-delayed systems employing generalized overflow nonlinearities. Nonlinear Analysis: Theory, Methods & Applications69(9): 2780–2787.
20.
KandanvliVKRKarH (2009) Robust stability of discrete-time state-delayed systems with saturation nonlinearities: Linear matrix inequality approach. Signal Processing89(2): 161–173.
21.
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.
22.
KandanvliVKRKarH (2013) Delay-dependent stability criterion for discrete-time uncertain state-delayed systems employing saturation nonlinearities. Arabian Journal for Science and Engineering38(10): 2911–2920.
23.
KanieskiJMCardosoRPinheiroHGründlingHA (2013) Kalman filter-based control system for power quality conditioning devices. IEEE Transactions on Industrial Electronics60(11): 5214–5227.
24.
KarH (2007) An LMI based criterion for the nonexistence of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic. Digital Signal Processing17(3): 685-689.
25.
KarHSinghV (2004) Elimination of overflow oscillations in fixed-point state-space digital filters with saturation arithmetic: An LMI approach. IEEE Transactions on Circuits and Systems II: Express Briefs51(1): 40–42.
26.
KiaminiSJalilvandAMobayenS (2018) LMI-based robust control of floating tension-leg platforms with uncertainties and time-delays in offshore wind turbines via T-S fuzzy approach. Ocean Engineering154: 367–374.
27.
KokilPArockiarajSX (2016) An improved criterion for induced stability of fixed-point digital filters with saturation arithmetic. Indonesian Journal of Electrical Engineering and Computer Science4(1): 65–72.
28.
KokilPArockiarajSX (2017) Novel results for induced stability for digital filters with external noise. Fluctuation and Noise Letters16(4): 1–18.
29.
KokilPArockiarajSXKarH (2018a) Criterion for limit cycle-free state-space digital filters with external disturbances and generalized overflow non-linearities. Transactions of the Institute of Measurement and Control40(4): 1158–1166.
30.
KokilPArockiarajSXJogiSKarH (2018b) New realizability criterion for digital filters with external disturbance and saturation arithmetic. AEÜ - International Journal of Electronics and Communications85: 179–182.
31.
KokilPJogiSAhnCK (2018c) Stability analysis of digital filters subjected to interference using generalized overflow nonlinearities. Signal Processing148: 1–8.
32.
KokilPKandanvliVKRKarH (2012) A note on the criterion for the elimination of overflow oscillations in fixed-point digital filters with saturation arithmetic and external disturbance. AEÜ - International Journal of Electronics and Communications66(9): 780–783.
33.
KokilPKarH (2012) An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic. Digital Signal Processing22(6): 1063–1067.
34.
KokilPKarHKandanvliVKR (2011) Stability analysis of discrete-time state-delayed systems with saturation nonlinearities. In: Proceedings of IEEE International Conference on Computational Intelligence and Computing Research, Kanyakumari, India.
35.
KokilPParthipanCGJogiSKarH (2019) Criterion for realizing state-delayed digital filters subjected to external interference employing saturation arithmetic. Cluster Computing22: 15187–15194.
36.
KokilPShindeSS (2015) Asymptotic stability of fixed-point state-space digital filters with saturation arithmetic and external disturbance: An IOSS approach. Circuits, Systems and Signal Processing34(12): 3965–3977.
37.
KumarMKKokilPKarH (2019) Novel ISS criteria for digital filters using generalized overflow non-linearities and external interference. Transactions of the Institute of Measurement and Control41(1): 156–164.
38.
LeeJ (2002) Constructive and discrete versions of the Lyapunov’s stability theorem and the LaSalle’s invariance theorem. Communications of the Korean Mathematical Society17(1): 155–163.
39.
LeeSMKwonOMParkJH (2012) Regional asymptotic stability analysis for discrete-time delayed systems with saturation nonlinearity. Nonlinear Dynamics67(1): 885–892.
40.
LiSWuJ (2015) Stochastic resonance in a bacterium growth system with time delay and colored noise. Fluctuation and Noise Letters14(2): 1–18.
41.
LiTSunNLinQLiJ (2012) Improved criterion for the elimination of overflow oscillations in digital filters with external disturbance. Advances in Difference Equations. 2012(1): 1–6.
42.
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.
43.
LiuLYinSZhangLet al. (2017c) Improved results on asymptotic stabilization for stochastic nonlinear time-delay systems with application to a chemical reactor system. IEEE Transactions on Systems, Man, and Cybernetics: Systems47(1): 195–204.
44.
LiuLJiaZYangJKasabovN (2017a) A remote sensing image enhancement method using mean filter and unsharp masking in non-subsampled contourlet transform domain. Transactions of the Institute of Measurement and Control39(2): 183–193.
45.
LiuRXuHZhengEJiangY (2017b) Adaptive filtering for intelligent sensing speech based on multi-rate LMS algorithm. Cluster Computing20(2): 1493–1503.
46.
LiuSBaşarTSrikantR (2008) TCP-Illinois: A loss- and delay-based congestion control algorithm for high-speed networks. Performance Evaluation65(6–7): 417–440.
47.
LuoYWangZWeiGAlsaadiFE (2017) Robust filtering for a class of two-dimensional uncertain fuzzy systems with randomly occurring mixed delays. IEEE Transactions on Fuzzy Systems25(1): 70–83.
48.
MitraSKEkstromMP (1978) Two-dimensional Digital Signal Processing. Dowden: Hutchinson & Ross.
49.
MobayenS (2016) Optimal LMI-based state feedback stabilizer for uncertain nonlinear systems with time-varying uncertainties and disturbances. Complexity21(6): 356–362.
50.
MobayenSTchierF (2016) An LMI approach to adaptive robust tracker design for uncertain nonlinear systems with time-delays and input nonlinearities. Nonlinear Dynamics85(3): 1965–1978.
51.
MoraisCFBragaMFOliveiraRCLFPeresPLD (2015) state feedback control for MJLS with uncertain probabilities. Automatica52: 317–321.
52.
PalVCNegiR (2018) Delay-dependent stability criterion for uncertain discrete time systems in presence of actuator saturation. Transactions of the Institute of Measurement and Control40(6): 1873–1891.
53.
ParthipanCGArockiarajSXKokilP (2018) New passivity results for the realization of interfered digital filters utilizing saturation overflow nonlinearities. Transactions of the Institute of Measurement and Control40(15): 4246–4252.
54.
PaszkeWLamJGalkowskiKXuSLinZ (2004) Robust stability and stabilisation of 2D discrete state-delayed systems. Systems & Control Letters51(3–4): 277–291.
55.
RehanMMobeenMBTufailMAhnCK (2018) A novel method for guaranteed overflow oscillation elimination in digital filters subject to quantization. IEEE Transactions on Circuits and Systems II: Express Briefs65(9): 1279–1283.
56.
SchlichtharleD (2001) Digital Filters: Basics and Design. Berlin, Germany: Springer.
57.
SinghV (1985) A new realizability condition for limit cycle-free state-space digital filters employing saturation arithmetic. IEEE Transactions on Circuits and Systems32(10): 1070–1071.
58.
SinghV (2006) Elimination of overflow oscillations in fixed-point state-space digital filters using saturation arithmetic: An LMI approach. Digital Signal Processing16(1): 45–51.
SuLChesiG (2018) On the design of output feedback controllers for LTI systems over fading channels. IEEE Transactions on Automatic Control63(5): 1503–1508.
61.
TadepalliSKKandanvliVKRKarH (2014) Stability criteria for uncertain discrete-time systems under the influence of saturation nonlinearities and time-varying delay. ISRN Applied Mathematics2014: 1–10.
62.
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.
63.
WangKWangYLiS (2017) Stability and stochastic resonance for a time-delayed cancer development system subjected to noises and multiplicative periodic signal. Fluctuation and Noise Letters16(3): 1–16.
64.
WenSXingLHuXZhangH (2017) Measurement-converted Kalman filter tracking with Gaussian intensity attenuation signal in wireless sensor networks. International Journal of Distributed Sensor Networks13(4): 1–13.
65.
WuLWangZ (2015) Filtering and Control for Classes of Two-Dimensional Systems. London, UK: Springer.
66.
WuZGShenYShiPet al. (2019) control for 2-D Markov jump systems in Roesser model. IEEE Transactions on Automatic Control64(1): 427–432.
67.
XiaWZhengWXXuS (2019) Realizability condition for digital filters with time delay using generalized overflow arithmetic. IEEE Transactions on Circuits and Systems II: Express Briefs66(1): 141–145.
68.
YangDCaiKY (2010) Reliable guaranteed cost sampling control for nonlinear time-delay systems. Mathematics and Computers in Simulation80(10): 2005–2018.
