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Network-based \(H_\infty\) filtering using a logic jumping-like trigger. (English) Zbl 1319.93076
Summary: This paper is concerned with the network-based \(H_\infty\) filtering for a stochastic system, where data transmission from the stochastic system to a filter is completed via a communication network. Network-induced delays, packet dropouts and packet disorders are unavoidable due to the use of the network. First, a logic zero-order-hold (ZOH) is designed to discard the disordered packets actively. The network-induced delays and packet dropouts are modeled as an interval time-varying delay. By decomposing the delay interval into \(N\) subintervals uniformly, the filter to be designed is modeled as a Markov jumping filter with \(N\) modes governed by a Markov chain. In order to work out the transition rate from one mode to another, a logic jumping-like trigger is embedded into the logic ZOH to simulate the switching of the Markov process. Second, based on the Markov jumping filter model together with a new integral inequality in the stochastic setting, a novel bounded real lemma is presented to ensure that the resultant filtering error system is mean exponentially stable with a prescribed \(H_\infty\) performance. Then, a sufficient condition on the existence of desired Markov jumping filters is provided in terms of a set of linear matrix inequalities. Finally, an air vehicle system is employed to show effectiveness of the proposed design method.

MSC:
93E11 Filtering in stochastic control theory
93B36 \(H^\infty\)-control
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[1] Chang, X.-H.; Yang, G.-H., Nonfragile \(\mathcal{H}_\infty\) filtering of continuous-time fuzzy systems, IEEE Transactions on Signal Processing, 59, 4, 1528-1538, (2011) · Zbl 1391.93134
[2] de Souza, C. E.; Trofino, A.; Barbosa, K. A., Mode-independent \(\mathcal{H}_\infty\) filters for Markovian jump linear systems, IEEE Transactions on Automatic Control, 51, 11, 1837-1841, (2006) · Zbl 1366.93666
[3] Gao, H.; Chen, T., \(\mathcal{H}_\infty\) estimation for uncertain systems with limited communication capacity, IEEE Transactions on Automatic Control, 52, 11, 2070-2084, (2007) · Zbl 1366.93155
[4] Geromel, J. C.; Bernussou, J.; Garcia, G.; de Oliveira, M. C., \(H_2\) and \(\mathcal{H}_\infty\) robust filtering for discrete-time linear systems, SIAM Journal on Control Optimization, 38, 5, 1353-1368, (1999) · Zbl 0958.93091
[5] Hung, Y. S.; Yang, F., Robust \(\mathcal{H}_\infty\) filtering with error variance constraints for discrete time-varying systems with uncertainty, Automatica, 39, 7, 1185-1194, (2003) · Zbl 1022.93046
[6] Li, H.; Shi, Y., Robust \(H_\infty\) filtering for nonlinear stochastic systems with uncertainties and Markov delays, Automatica, 48, 1, 159-166, (2012) · Zbl 1244.93158
[7] Ma, L.; Da, F.; Zhang, K., Exponential \(\mathcal{H}_\infty\) filter design for discrete time-delay stochastic systems with Markovian jump parameters and missing measurements, IEEE Transactions on Circuit Systems I: Regular Papers, 58, 3, 994-1007, (2011)
[8] Mao, X., Stochastic differential equations and their applications, (1997), Horwood Chichester, UK
[9] Sahebsara, M.; Chen, T.; Shah, S., Optimal \(\mathcal{H}_\infty\) filtering in networked control systems with multiple packet dropouts, Systems & Control Letters, 57, 9, 696-702, (2008) · Zbl 1153.93034
[10] Shao, H., Delay-range-dependent robust \(\mathcal{H}_\infty\) filtering for uncertain stochastic systems with mode-dependent time delays and Markovian jump parameters, Journal of Mathematical Analysis and Applications, 342, 2, 1084-1095, (2008) · Zbl 1141.93025
[11] Wang, Z.; Liu, Y.; Liu, X., \(\mathcal{H}_\infty\) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica, 44, 5, 1268-1277, (2008) · Zbl 1283.93284
[12] Wang, Z.; Yang, F.; Ho, D. W.C., Robust \(\mathcal{H}_\infty\) filtering for stochastic time-delay systems with missing measurements, IEEE Transactions on Signal Processing, 54, 7, 2579-2587, (2006) · Zbl 1373.94729
[13] Wu, H.-N.; Wang, J.-W.; Shi, P., A delay decomposition approach to \(\mathcal{L}_2 - \mathcal{L}_\infty\) filter design for stochastic systems with time-varying delay, Automatica, 47, 7, 1482-1488, (2011) · Zbl 1220.93077
[14] Xie, L.; Lu, L.; Zhang, D.; Zhang, H. S., Improved robust \(H_2\) and \(\mathcal{H}_\infty\) filtering for uncertain discrete-time systems, Automatica, 40, 5, 873-880, (2004) · Zbl 1050.93072
[15] Xiong, J.; Lam, J., Stabilization of networked control systems with a logic ZOH, IEEE Transactions on Automatic Control, 54, 2, 358-363, (2009) · Zbl 1367.93546
[16] Yaesh, I., Shaked, U., & Yossef, T. (2004). Simplified adaptive control of F16 aircraft pitch and angle-of-attack loops. In Proceedings of the 44th Israel annual conference on aerospace sciences (pp. 25-26). Haifa, Israel.
[17] Yang, R.; Shi, P.; Liu, G.-P., Filtering for discrete-time networked nonlinear systems with mixed random delays and packet dropouts, IEEE Transactions on Automatic Control, 56, 11, 2655-2660, (2011) · Zbl 1368.93734
[18] Yue, D.; Han, Q.-L., Network-based robust \(\mathcal{H}_\infty\) filtering for uncertain linear systems, IEEE Transactions on Signal Processing, 54, 11, 4293-4301, (2006) · Zbl 1373.93111
[19] Zhang, H.; Chen, Q.; Yan, H.; Liu, J., Robust \(\mathcal{H}_\infty\) filtering for switched stochastic system with missing measurements, IEEE Transactions on Signal Processing, 57, 9, 3466-3474, (2009) · Zbl 1391.93263
[20] Zhang, X.-M.; Han, Q.-L., A delay decomposition appraoch to \(\mathcal{H}_\infty\) control of networked control systems, European Journal of Control, 15, 5, 523-533, (2009)
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