\(H_\infty\) filtering of networked discrete-time systems with random packet losses. (English) Zbl 1187.93132

Summary: This paper studies the \(H_\infty\) filtering problem for networked discrete-time systems with random packet losses. The general Multiple-Input-Multiple-Output (MIMO) filtering system is considered. The multiple measurements are transmitted to the remote filter via distinct communication channels, and each measurement loss process is described by a two-state Markov chain. Both the mode-independent and the mode-dependent filters are considered, and the resulting filtering error system is modelled as a discrete-time Markovian system with multiple modes. A necessary and sufficient condition is derived for the filtering error system to be mean-square exponentially stable and achieve a prescribed \(H_\infty\) noise attenuation performance. The obtained condition implicitly establishes a relation between the packet loss probability and two parameters, namely, the exponential decay rate of the filtering error system and the \(H_\infty\) noise attenuation level. A convex optimization problem is formulated to design the desired filters with minimized \(H_\infty\) noise attenuation level bound. Finally, an illustrative example is given to show the effectiveness of the proposed results.


93E11 Filtering in stochastic control theory
93C55 Discrete-time control/observation systems
90B18 Communication networks in operations research
60J05 Discrete-time Markov processes on general state spaces
90C25 Convex programming
Full Text: DOI


[1] Gao, H. J.; Chen, T. W., \(H_∞\) estimation for uncertain systems with limited communication capacity, IEEE Trans. Automat. Contr., 52, 11, 2070-2080 (2007) · Zbl 1366.93155
[2] Gao, H. J.; Lam, J.; Chen, T. W.; Wang, C. H., Feedback control with signal transmission after-effects, Int. J. Robust Nonlin. Contr., 18, 3, 351-363 (2008) · Zbl 1284.93108
[3] Geromel, J. C.; de Oliveira, M. C.; Bernussou, J., Robust filtering of discrete-time linear systems with parameter dependent Lyapunov functions, SIAM J. Contr. Optim., 41, 3, 700-711 (2002) · Zbl 1022.93048
[4] Hu, L. S.; Bai, T.; Shi, P.; Wu, Z. M., Sampled-data control of networked linear control systems, Automatica, 43, 5, 903-911 (2007) · Zbl 1117.93044
[5] Jin, Z. P.; Gupta, V.; Murray, R. M., State estimation over packet dropping networks using multiple description coding, Automatica, 42, 9, 1441-1452 (2006) · Zbl 1128.93051
[6] Lin, H.; Antsaklis, P. J., Stability and persistent disturbance attenuation properties for a class of networked control systems: switched system approach, Int. J. Contr., 78, 18, 1447-1458 (2005) · Zbl 1122.93357
[7] Lorand, C.; Bauer, P. H., On synchronization errors in networked feedback systems, IEEE Trans. Circ. Syst., Regular Paper, 53, 10, 2306-2317 (2006) · Zbl 1374.93303
[8] Lian, F. L.; Moyne, J. R.; Tilbury, D. M., Performance evaluation of control networks: Ethernet ControlNet DeviceNet, IEEE Contr. Syst. Mag., 21, 1, 66-83 (2001)
[9] Liu, G. P.; Xia, Y.; Chen, J.; Rees, D.; Hu, W. S., Networked predictive control of systems with random network delays in both forward and feedback channels, IEEE Trans. Ind. Electron., 54, 3, 1282-1297 (2007)
[10] Matveev, A.; Savkin, A., The problem of state estimation via asynchronous communication channels with irregular transmission times, IEEE Trans. Automat. Contr., 48, 4, 670-676 (2003) · Zbl 1364.93779
[12] Peng, C.; Tian, Y. C., Networked \(H_∞\) control of linear systems with state quantization, Inform. Sci., 177, 24, 5763-5774 (2007) · Zbl 1126.93338
[13] Savkin, A. V., Analysis and synthesis of networked control systems: topology entropy observability robustness and optimal control, Automatica, 42, 1, 51-56 (2006) · Zbl 1121.93321
[14] Sahebsara, M.; Chen, T. W.; Shan, S. L., Optimal filtering with random sensor delay multiple packet dropout and uncertain observations, Int. J. Contr., 80, 2, 292-301 (2007) · Zbl 1140.93486
[15] Sahebsara, M.; Chen, T. W.; Shah, S. L., Optimal \(H_∞\) filtering in networked control systems with multiple packet dropouts, Syst. Contr. Lett., 57, 9, 696-702 (2008) · Zbl 1153.93034
[16] Seiler, P.; Sengupta, R., A bounded real lemma for jump systems, IEEE Trans. Automat. Contr., 48, 9, 1651-1654 (2003) · Zbl 1364.93223
[17] Smith, S.; Seiler, P., Estimation with lossy measurements: jump estimators for jump systems, IEEE Trans. Automat. Contr., 48, 12, 2163-2171 (2003) · Zbl 1364.93785
[18] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M. I.; Sastry, S. S., Kalman filtering with intermittent observations, IEEE Trans. Automat. Contr., 49, 9, 1453-1464 (2004) · Zbl 1365.93512
[19] Tian, Y. C.; Levy, D., Compensation for control packet dropout in networked control systems, Inform. Sci., 178, 5, 1263-1278 (2008) · Zbl 1139.93300
[20] Tian, E. G.; Yue, D.; Peng, C., Quantized output feedback control for networked control systems, Inform. Sci., 178, 12, 2734-2749 (2008) · Zbl 1179.93096
[21] Wang, Z. D.; Ho, D. W.C.; Liu, X. H., Variance-constrained filtering for uncertain stochastic systems with missing measurements, IEEE Trans. Automat. Contr., 48, 7, 1254-1258 (2003) · Zbl 1364.93814
[22] Yue, D.; Han, Q. L., Network-based robust \(H_∞\) filtering for uncertain linear systems, IEEE Trans. Signal Process., 54, 11, 4293-4301 (2006) · Zbl 1373.93111
[23] Zhang, W.; Branicky, M. S.; Phillips, S. M., Stability analysis of networked control systems, IEEE Contr. Syst. Mag., 21, 1, 84-99 (2001)
[24] Zhou, S. S.; Feng, G., \(H_∞\) filtering for discrete-time systems with randomly varying sensor delays, Automatica, 44, 7, 1918-1922 (2008) · Zbl 1149.93347
[25] Zhang, L. Q.; Shi, Y.; Chen, T. W.; Huang, B., A new method for stabilization of networked control systems with random delays, IEEE Trans. Automat. Contr., 50, 8, 1177-1181 (2005) · Zbl 1365.93421
[26] Zhang, W. A.; Yu, L., Output feedback stabilization of networked control systems with packet dropouts, IEEE Trans. Automat. Contr., 52, 9, 1705-1710 (2007) · Zbl 1366.93543
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.