zbMATH — the first resource for mathematics

A novel Wirtinger-based inequality to \(H_\infty\) filtering for discrete-time systems with time-varying delay. (English) Zbl 1435.93099
Summary: This article is committed to \(H_{\infty}\) filtering for linear discrete-time systems with time-varying delay. The novelty of the paper comes from the consideration of the new Wirtinger-based inequality with double accumulation terms and the idea of delay-partitioning, which guarantees a better asymptotic stability and is less conservative than the celebrated free-weighting matrix or Jensen’s inequality methods. In combination with the improved Wirtinger-based inequality to handle the modified Lyapunov-Krasovskii (L-K) functionals, a new delay-dependent bound real lemma (BRL) is gained. In the light of the derived \(H_{\infty}\) performance analysis results, the \(H_{\infty}\) filter will be designed in response to linear matrix inequality (LMI). The validness of the proposed methods will be expressed via some numerical examples by the comparison of existing results.
93C55 Discrete-time control/observation systems
26D15 Inequalities for sums, series and integrals
93B07 Observability
93B36 \(H^\infty\)-control
93C73 Perturbations in control/observation systems
Full Text: DOI
[1] Qiu, J.; Feng, G.; Yang, J., Improved delay-dependent H∞ filtering design for discrete-time polytopic linear delay systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 55, 2, 178-182 (2008)
[2] Zhang, X.-M.; Han, Q.-L., Delay-dependent robust H∞ filtering for uncertain discrete-time systems with time-varying delay based on a finite sum inequality, IEEE Transactions on Circuits and Systems II: Express Briefs, 53, 12, 1466-1470 (2006)
[3] Xu, S., Robust \(H_\infty\) filtering for a class of discrete-time uncertain nonlinear systems with state delay, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 49, 12, 1853-1859 (2002)
[4] Zoulagh, T.; El Aiss, H.; Hmamed, A.; El Hajjaji, A., \(H_∞\) filter design for discrete time-varying delay systems: three-term approximation approach, IET Control Theory & Applications, 12, 2, 254-262 (2018)
[5] Ishihara, J. Y.; Terra, M. H.; Espinoza, B. M., \(H_∞\) filtering for rectangular discrete-time descriptor systems, Automatica, 45, 7, 1743-1748 (2009) · Zbl 1184.93112
[6] He, Y.; Liu, G.-P.; Rees, D.; Wu, M., \(H_∞\) filtering for discrete-time systems with time-varying delay, Signal Processing, 89, 3, 275-282 (2009) · Zbl 1151.94369
[7] Yan, H. C.; Yang, Q.; Zhang, H.; Yang, F. W.; Zhan, X. S., Distributed H∞ state estimation for a class of filtering networks with time-varying switching topologies and packet losses, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 99, 1-11 (2017)
[8] Chang, X.; Yang, G., Robust H-infinity filtering for uncertain discrete-time systems using parameter-dependent Lyapunov functions, Control Theory and Technology, 11, 1, 122-127 (2013)
[9] An, X.; Zhang, W.; Li, Q., \(H_∞\) filtering of stochastic time-delay systems with state dependent noise, Asian Journal of Control, 10, 3, 384-391 (2008)
[10] You, J.; Gao, H.; Basin, M. V., Further improved results on H-infinity filtering for discrete time-delay systems, Signal Processing, 93, 7, 1845-1852 (2013)
[11] Zhang, H.; Zheng, X.; Yan, H.; Peng, C.; Wang, Z.; Chen, Q., Codesign of event-triggered and distributed H∞ filtering for active semi-vehicle suspension systems, IEEE/ASME Transactions on Mechatronics, 22, 2, 1047-1058 (2017)
[12] Qiu, J.; Feng, G.; Yang, J., Delay-dependent non-synchronized robust H∞ state estimation for discrete-time piecewise linear delay systems, International Journal of Adaptive Control and Signal Processing, 23, 12, 1082-1096 (2009) · Zbl 1191.93132
[13] Gao, H.; Meng, X.; Chen, T., H∞ filter design for discrete delay systems: a new parameter-dependent approach, International Journal of Control, 82, 6, 993-1005 (2009) · Zbl 1168.93368
[14] Matsunaga, H., Delay-dependent and delay-independent stability criteria for a delay differential system, Proceedings of the American Mathematical Society, 136, 12, 4305-4312 (2008) · Zbl 1162.34061
[15] Debeljkovic, D.; Stojanovic, S.; Dimitrijevic, N., Stability of time-delay systems in the sense of non-lyapunov delay-independent and delay-dependent criteria, Tehnika, 67, 3, 385-393 (2012)
[16] Zhang, X.-M.; Wu, M.; Man, Q.-L.; She, J.-H., A new integral inequality approach to delay-dependent robust \(H_∞\) control, Asian Journal of Control, 8, 2, 153-160 (2006)
[17] Wang, D.; Shi, P.; Wang, J.; Wang, W., Delay-dependent exponential \(H_∞\) filtering for discrete-time switched delay systems, International Journal of Robust and Nonlinear Control, 22, 13, 1522-1536 (2012) · Zbl 1287.93096
[18] Zhang, C.-K.; He, Y.; Jiang, L.; Lin, W.-J.; Wu, M., Delay-dependent stability analysis of neural networks with time-varying delay: a generalized free-weighting-matrix approach, Applied Mathematics and Computation, 294, 102-120 (2017) · Zbl 1411.92012
[19] Federherr, E.; Kupka, H. J.; Cerli, C.; Kalbitz, K.; Dunsbach, R.; Loos, A.; de Reus, M.; Lange, L.; Panetta, R. J.; Schmidt, T. C., A novel tool for stable nitrogen isotope analysis in aqueous samples, Rapid Communications in Mass Spectrometry, 30, 23, 2537-2544 (2016)
[20] Hahn, J.; Edgar, T. F.; Marquardt, W., Controllability and observability covariance matrices for the analysis and order reduction of stable nonlinear systems, Journal of Process Control, 13, 2, 115-127 (2003)
[21] Nam, P. T.; Pathirana, P. N.; Trinh, H., Discrete Wirtinger-based inequality and its application, Journal of The Franklin Institute, 352, 5, 1893-1905 (2015) · Zbl 1395.93448
[22] Zhang, Y.; Liang, H.; Ma, H.; Zhou, Q.; Yu, Z., Distributed adaptive consensus tracking control for nonlinear multi-agent systems with state constraints, Applied Mathematics and Computation, 326, 16-32 (2018) · Zbl 1426.93168
[23] Ma, H.; Zhou, Q.; Bai, L.; Liang, H., Observer-based adaptive fuzzy fault-tolerant control for stochastic nonstrict-feedback nonlinear systems with input quantization, IEEE Transactions on Systems, Man, and Cybernetics: Systems (2019)
[24] Yan, H.; Zhou, X.; Zhang, H.; Yang, F.; Wu, Z., A novel sliding mode estimation for microgrid control with communication time delays, IEEE Transactions on Smart Grid, 1-1 (2017)
[25] Tong, M. S.; Pan, Y. L.; Li, Z.; Lin, W. L., Valid data based normalized cross-correlation (VDNCC) for topography identification, Neurocomputing, 316, 313-321 (2018)
[26] Zheng, Z.; Sun, L.; Xie, L., Error-constrained Los path following of a surface vessel with actuator saturation and faults, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 48, 10, 1794-1805 (2018)
[27] Zheng, Z.; Huang, Y.; Xie, L.; Zhu, B., Adaptive trajectory tracking control of a fully actuated surface vessel with asymmetrically constrained input and output, IEEE Transactions on Control Systems Technology, 26, 5, 1851-1859 (2018)
[28] Lee, C.; Yeh, C.; Hong, C.; Agarwal, R. P., Lyapunov and Wirtinger inequalities, Applied Mathematics Letters, 17, 7, 847-853 (2004) · Zbl 1062.34005
[29] Li, X.; Li, Z.; Gao, H., Further results on H∞ filtering for discrete-time systems with state delay, International Journal of Robust and Nonlinear Control, 21, 3, 248-270 (2011) · Zbl 1213.93124
[30] Meng, X.; Lam, J.; Du, B.; Gao, H., A delay-partitioning approach to the stability analysis of discrete-time systems, Automatica, 46, 3, 610-614 (2010) · Zbl 1194.93131
[31] Lian, K.-Y.; Yang, W.-T.; Liu, P., Partitioning technique for relaxed stability criteria of discrete-time systems with interval time-varying delay, Discrete Dynamics in Nature and Society, 2014 (2014) · Zbl 1419.93038
[32] He, Y.; Wang, Q. G.; Xie, L. H.; Lin, C., Further improvement of free-weighting matrices technique for systems with time-varying delay, IEEE Transactions on Automatic Control, 52, 2, 293-299 (2007) · Zbl 1366.34097
[33] Briat, C., Convergence and equivalence results for the Jensen’s inequality—application to time-delay and sampled-data systems, IEEE Transactions on Automatic Control, 56, 7, 1660-1665 (2011) · Zbl 1368.26020
[34] Seuret, A.; Gouaisbaut, F.; Fridman, E., Stability of discrete-time systems with time-varying delays via a novel summation inequality, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 60, 10, 2740-2745 (2015) · Zbl 1360.93612
[35] Chen, J.; Xu, S.; Jia, X.; Zhang, B., Novel summation inequalities and their applications to stability analysis for systems with time-varying delay, Institute of Electrical and Electronics Engineers Transactions on Automatic Control, 62, 5, 2470-2475 (2017) · Zbl 1366.93432
[36] Zhang, X.-M.; Han, Q.-L.; Seuret, A.; Gouaisbaut, F., An improved reciprocally convex inequality and an augmented Lyapunov-Krasovskii functional for stability of linear systems with time-varying delay, Automatica, 84, 221-226 (2017) · Zbl 1375.93114
[37] Wei, Y.; Qiu, J.; Shi, P.; Chadli, M., Fixed-order piecewise-affine output feedback controller for fuzzy-affine-model-based nonlinear systems with time-varying delay, IEEE Transactions on Circuits and Systems I: Regular Papers, 64, 4, 945-958 (2017)
[38] Wei, Y.; Qiu, J.; Karimi, H. R., Fuzzy-affine-model-based memory filter design of nonlinear systems with time-varying delay, IEEE Transactions on Fuzzy Systems, 26, 2, 504-517 (2018)
[39] Xiao, S.; Xu, L.; Zeng, H.; Teo, K. L., Improved stability criteria for discrete-time delay systems via novel summation inequalities, International Journal of Control, Automation, and Systems, 16, 4, 1592-1602 (2018)
[40] de Oliveira, M. C.; Bernussou, J.; Geromel, J. C., A new discrete-time robust stability condition, Systems & Control Letters, 37, 4, 261-265 (1999) · Zbl 0948.93058
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.