\(h\)-stability-based \(l_2-l_\infty\) state estimation of discrete-time nonlinear systems with time-varying delays. (English) Zbl 1541.93352
Summary: In this paper, the \(l_2-l_\infty\) state estimation problem of discrete-time nonlinear systems (DTNSs) with time-varying delay is studied. The main objective of this paper is to design a state estimator that guarantees not only the global \(h\)-stability of the error system in the absence of interference, but also that the output peak value of the error system remains within a certain range under the zero initial conditions. A direct analysis method based on the system solutions is presented, which gives a sufficient condition to decide whether the designed state estimator satisfies the expectation. The method does not follow the construct of any Lyapunov-Krasovskii functional (LKF), thus greatly reducing the workload and complexity of calculation. Finally, three simulation examples are presented to illustrate the applicability of the theoretical results.
MSC:
| 93E10 | Estimation and detection in stochastic control theory |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 93C55 | Discrete-time control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93C43 | Delay control/observation systems |
Keywords:
discrete-time nonlinear systems; \(l_2-l_\infty\) state estimation; global \(h\)-stability; a direct method based on system solutionsReferences:
| [1] | Li, Y.-G.; Yang, G.-H., Optimal innovation-based deception attacks with side information against remote state estimation in cyber-physical systems, Neurocomputing, 500, 461-470, 2022 |
| [2] | Wang, X.; Park, J. H.; Liu, H.; Zhang, X., Cooperative output-feedback secure control of distributed linear cyber-physical systems resist intermittent DoS attacks, IEEE Trans. Cybern., 51, 10, 4924-4933, 2021 |
| [3] | Zhang, X.; Han, Y.; Wu, L.; Wang, Y., State estimation for delayed genetic regulatory networks with reaction-diffusion terms, IEEE Trans. Neural Netw. Learn. Syst., 29, 2, 299-309, 2018 |
| [4] | Zhang, X.; Fan, X.; Wu, L., Reduced- and full-order observers for delayed genetic regulatory networks, IEEE Trans. Cybern., 48, 7, 1989-2000, 2018 |
| [5] | Li, X.; Li, F.; Zhang, X.; Yang, C.; Gui, W., Exponential stability analysis for delayed semi-Markovian recurrent neural networks: A homogeneous polynomial approach, IEEE Trans. Neural Netw. Learn. Syst., 29, 12, 6374-6384, 2018 |
| [6] | Dong, Z.; Wang, X.; Zhang, X.; Hu, M.; Dinh, T. N., Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption, Nonlinear Anal. Hybrid Syst., 47, 2023, Article No. 101291 · Zbl 1505.93206 |
| [7] | Dong, Z.; Wang, X.; Zhang, X., A nonsingular M-matrix-based global exponential stability analysis of higher-order delayed discrete-time Cohen-Grossberg neural networks, Appl. Math. Comput., 385, 2020, Article No. 125401 · Zbl 1508.39013 |
| [8] | Xue, Y.; Liu, C.; Zhang, X., State bounding description and reachable set estimation for discrete-time genetic regulatory networks with time-varying delays and bounded disturbances, IEEE Trans. Syst. Man Cybern: Syst., 52, 10, 6652-6661, 2022 |
| [9] | Wang, J.; Wang, X.; Zhang, X.; Zhu, S., Global \(h\)-synchronization of high-order delayed inertial neural networks via direct SORS approach, IEEE Trans. Syst. Man Cybern: Syst., 53, 11, 6693-6704, 2023 |
| [10] | Liu, Y.; Shen, B.; Zhang, P., Synchronization and state estimation for discrete-time coupled delayed complex-valued neural networks with random system parameters, Neural Netw., 150, 181-193, 2022 · Zbl 1525.93327 |
| [11] | Wang, X.; Yang, G. H., Fault-tolerant consensus tracking control for linear multiagent systems under switching directed network, IEEE Trans. Cybern., 50, 5, 1921-1930, 2020 |
| [12] | Wang, J.; Zhang, X.; Wang, X.; Yang, X., \( L_2 - L_\infty\) state estimation of the high-order inertial neural network with time-varying delay: Non-reduced order strategy, Inform. Sci., 607, 62-78, 2022 · Zbl 1533.93785 |
| [13] | Shen, H.; Wang, T.; Chen, M.; Lu, J., Nonfragile mixed \(H_\infty/ l_2 - l_\infty\) state estimation for repeated scalar nonlinear systems with Markov jumping parameters and redundant channels, Nonlinear Dynam., 91, 1, 641-654, 2018 · Zbl 1390.93289 |
| [14] | Lin, W.-J.; He, Y.; Zhang, C.-K.; Wu, M., Stochastic finite-time \(H_\infty\) state estimation for discrete-time semi-Markovian jump neural networks with time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 31, 12, 5456-5467, 2020 |
| [15] | Li, R.; Cao, J., Exponential \(H_\infty\) state estimation for memristive neural networks: Vector optimization approach, IEEE Trans. Neural Netw. Learn. Syst., 32, 11, 5061-5071, 2020 |
| [16] | Wang, Z.; Liu, H.; Shen, B.; Alsaadi, F. E.; Dobaie, A. M., \( H_\infty\) state estimation for discrete-time stochastic memristive BAM neural networks with mixed time-delays, Int. J. Mach. Learn. & Cybern., 10, 4, 771-785, 2019 |
| [17] | Wang, H.; Dong, R.; Xue, A.; Peng, Y., Event-triggered \(L_2 - L_\infty\) state estimation for discrete-time neural networks with sensor saturations and data quantization, J. Franklin Inst., 356, 17, 10216-10240, 2019 · Zbl 1425.93092 |
| [18] | Chen, Y.; Liu, L.; Qian, W.; Liu, Y.; Alsaadi, F. E., \( l_2 - l_\infty\) state estimation for discrete-time switched neural networks with time-varying delay, Neurocomputing, 282, 25-31, 2018 |
| [19] | Hou, L.; Zong, G.; Wu, Y., Robust exponential stability analysis of discrete-time switched hopfield neural networks with time delay, Nonlinear Anal. Hybrid Syst., 5, 3, 525-534, 2011 · Zbl 1238.93075 |
| [20] | Li, H.; Zhao, N.; Wang, X.; Zhang, X.; Shi, P., Necessary and sufficient conditions of exponential stability for delayed linear discrete-time systems, IEEE Trans. Autom. Control, 64, 2, 712-719, 2019 · Zbl 1482.39002 |
| [21] | Nasser, B. B.; Boukerrioua, K.; Defoort, M.; Djemai, M.; Hammami, M.; Lalegkirati, T., Sufficient conditions for uniform exponential stability and \(h\)-stability of some classes of dynamic equations on arbitrary time scales, Nonlinear Anal. Hybrid Syst., 32, 54-64, 2019 · Zbl 1427.34119 |
| [22] | Choi, S. K.; Koo, N. J.; Im, D. M., \(h\)-Stability for linear dynamic equations on time scales, J. Math. Anal. Appl., 324, 1, 707-720, 2006 · Zbl 1112.34031 |
| [23] | Pinto, M., Perturbations of asymptotically stable differential systems, Analysis (Munich), 4, 1-2, 161-176, 1984 · Zbl 0568.34035 |
| [24] | Wang, J.; Wang, X.; Wang, Y.; Zhang, X., Non-reduced order method to global \(h\)-stability criteria for proportional delay high-order inertial neural networks, Appl. Math. Comput., 407, 2021, Article No. 126308 · Zbl 1510.34163 |
| [25] | Choi, S. K.; Koo, N. J., Variationally stable difference systems by \(n_\infty \)-similarity, J. Math. Anal. Appl., 249, 2, 553-568, 2000 · Zbl 0965.39001 |
| [26] | Zhang, F.; Zeng, Z., Multiple \(\psi \)-type stability of Cohen-Grossberg neural networks with unbounded time-varying delays, IEEE Trans. Syst. Man Cybern: Syst., 51, 1, 521-531, 2018 |
| [27] | Wu, L.; Feng, Z.; Lam, J., Stability and synchronization of discrete-time neural networks with switching parameters and time-varying delays, IEEE Trans. Neural Netw. Learn. Syst., 24, 12, 1957-1972, 2013 |
| [28] | Zhang, X.-M.; Han, Q.-L.; Ge, X.; Zhang, B.-L., Delay-variation-dependent criteria on extended dissipativity for discrete-time neural networks with time-varying delay, IEEE Trans. Neural Netw. Learn. Syst., 1578-1587, 2021 |
| [29] | Tan, G.; Wang, Z.; Xiao, S., Nonfragile extended dissipativity state estimator design for discrete-time neural networks with time-varying delay, Neurocomputing, 539, 2023, Article No. 126206 |
| [30] | Zhao, P.; Liu, H.; He, G.; Ding, D., Outlier-resistant \(L_2 - L_\infty\) state estimation for discrete-time memristive neural networks with time-delays, Syst. Sci. Control Eng., 9, 1, 88-97, 2021 |
| [31] | Liu, H.; Wang, Z.; Fei, W.; Li, J., \( H_\infty\) and \(L_2 - L_\infty\) state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol, Neural Netw., 132, 121-130, 2020 · Zbl 1478.93151 |
| [32] | Ben-Israel, A.; Greville, T. N., Generalized Inverses: Theory and Applications, 2003, Springer Science & Business Media: Springer Science & Business Media New York · Zbl 1026.15004 |
| [33] | Wang, L.; Huang, T.; Xiao, Q., Lagrange stability of delayed switched inertial neural networks, Neurocomputing, 381, 52-60, 2020 |
| [34] | Liu, L.; Zhu, S.; Wu, B.; Wang, Y. E., On designing state estimators for discrete-time recurrent neural networks with interval-like time-varying delays, Neurocomputing, 286, 67-74, 2018 |
| [35] | Zhao, D.; Wang, Z.; Chen, Y.; Wei, G., Proportional-integral observer design for multidelayed sensor-saturated recurrent neural networks: A dynamic event-triggered protocol, IEEE Trans. Cybern., 50, 11, 4619-4632, 2020 |
| [36] | Elowitz, M. B.; Leibler, S., A synthetic oscillatory network of transcriptional regulators, Nature, 403, 6767, 335-338, 2000 |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
