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Networked \(H_\infty\) filtering under a weighted TOD protocol. (English) Zbl 1429.93397

Summary: This paper is concerned with the problem of networked \(H_\infty\) filtering under a weighted try-once-discard (TOD) protocol. Firstly, a weighted TOD protocol is investigated to orchestrate the sampled-data transmission from sensors to filter via a bandwidth-limited network. Taking into account the network-induced delay, the studied system is transformed into an impulsive system with an interval time-varying delay. Secondly, by using the Lyapunov-Krasovskii method, sufficient conditions for ensuring the exponential stability with a prescribed \(H_\infty\) performance and the existence of suitable \(H_\infty\) filter are obtained in the form of linear matrix inequalities (LMIs). Then, for minimizing \(H_\infty\) performance, an algorithm is presented by using the binary search method. Finally, an example of quarter-car model with an active suspension is used to verify the validity of proposed method.

MSC:

93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
93B70 Networked control
93C43 Delay control/observation systems
93D23 Exponential stability
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References:

[1] Antsaklis, P.; Baillieul, J., Special issue on technology of networked control systems, Proceedings of the IEEE, 95, 1, 5-8 (2007)
[2] Doostmohammadian, M., & Khan, U. A. (2013). Topology design in networked estimation: A generic approach. In American control conference; Doostmohammadian, M., & Khan, U. A. (2013). Topology design in networked estimation: A generic approach. In American control conference
[3] Doostmohammadian, M.; Khan, U. A., Graph-theoretic distributed inference in social networks, IEEE Journal of Selected Topics in Signal Processing, 8, 4, 613-623 (2014)
[4] Freirich, D.; Fridman, E., Decentralized networked control of systems with local networks: a time-delay approach, Automatica, 69, 201-209 (2016) · Zbl 1338.93019
[5] Fridman, E., Introduction to time-delay systems: analysis and control (2014), Birkhäuser: Birkhäuser Basel · Zbl 1303.93005
[6] Fridman, E.; Shaked, U.; Xie, L., Robust \(H_\infty\) filtering of linear systems with time-varying delay, IEEE Transactions on Automatic Control, 48, 1, 159-165 (2003) · Zbl 1364.93797
[7] Gu, K.; Chen, J.; Kharitonov, V. L., Stability of time-delay systems (2003), Springer Science & Business Media · Zbl 1039.34067
[8] Gupta, V.; Chung, T. H.; Hassibi, B.; Murray, R. M., On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage, Automatica, 42, 2, 251-260 (2006) · Zbl 1125.93486
[9] Lacerda, M. J.; Oliveira, R. C.; Peres, P. L., Robust \(H_2\) and \(H_\infty\) filter design for uncertain linear systems via LMIs and polynomial matrices, Signal Processing, 91, 5, 1115-1122 (2011) · Zbl 1222.93127
[10] Liu, K.; Fridman, E.; Hetel, L., Networked control systems in the presence of scheduling protocols and communication delays, SIAM Journal on Control and Optimization, 53, 4, 1768-1788 (2015) · Zbl 1317.93212
[11] Liu, K.; Fridman, E.; Johansson, K. H., Networked control with stochastic scheduling, IEEE Transactions on Automatic Control, 60, 11, 3071-3076 (2015) · Zbl 1360.93745
[12] Liu, K.; Seuret, A.; Fridman, E.; Xia, Y., Improved stability conditions for discrete-time systems under dynamic network protocols, International Journal of Robust and Nonlinear Control, 28, 15, 4479-4499 (2018) · Zbl 1401.93157
[13] Park, P.; Ko, J. W.; Jeong, C., Reciprocally convex approach to stability of systems with time-varying delays, Automatica, 47, 1, 235-238 (2011) · Zbl 1209.93076
[14] Peng, C.; Ma, S.; Xie, X., Observer-based non-PDC control for networked t-s fuzzy systems with an event-triggered communication, IEEE Transactions on Cybernetics, 47, 8, 2279-2287 (2017)
[15] Peng, C.; Q.-L., Han, On designing a novel self-triggered sampling scheme for networked control systems with network-induced delays and data dropouts, IEEE Transactions on Industrial Electronics, 63, 2, 1239-1248 (2016)
[16] Peng, C.; Sun, H.; Yang, M.; Wang, Y., A survey on security communication and control for smart grids under malicious cyber attacks, IEEE Transactions on Systems Man & Cybernetics: Systems (2019)
[17] Wang, Z.; Liu, Y.; Liu, X., \(H_\infty\) Filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 5, 1268-1277 (2008) · Zbl 1283.93284
[18] Wu, J.; Chen, X.; Gao, H., \(H_\infty\) Filtering with stochastic sampling, Signal Processing, 90, 4, 1131-1145 (2010) · Zbl 1197.94143
[19] Yue, D.; Han, Q.-L., Network-based robust \(H_\infty\) filtering for uncertain linear systems, IEEE Transactions on Signal Processing, 54, 11, 4293-4301 (2006) · Zbl 1373.93111
[20] Zhang, X.; Han, Q.-L., Event-based \(H_\infty\) filtering for sampled-data systems, Automatica, 51, 51, 55-69 (2015) · Zbl 1309.93096
[21] Zhang, J.; Peng, C.; Fei, M.-R.; Tian, Y.-C., Output feedback control of networked systems with a stochastic communication protocol, Journal of the Franklin Institute, 354, 9, 3838-3853 (2017) · Zbl 1367.93624
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