Filter Inputs With Markovian Lossy Links: Zero Or Hold?

This paper is concerned with 2 and ∞ filter design for discrete-time Markov jump systems. The Markov chain is used to model a lossy network and two different strategies used in practice are compared for the event of packet dropout. The zero-input strategy consists of providing the filter with null input in case of dropout, while the hold-input strategy consists of using the previous successfully transmitted value of the measurement as input in that case. We prove that both strategies are rigorously equivalent in terms of filtering performance. This result suggests that the zero-input strategy is always preferable than the hold-input strategy because its modeling is simpler and its implementation is cheaper than the latter. A numerical example illustrates the applicability of the results. © 2011 IEEE.656661Costa, O.L.V., Fragoso, M.D., Marques, R.P., (2005) Discrete-Time Markov Jump Linear Systems, , Springer-VerlagHespanha, J., Naghshtabrizi, P., Xu, Y., A survey of recent results in networked control systems (2007) Proceedings of the IEEE, 95, pp. 138-162Gonçalves, A.P.C., Fioravanti, A.R., Geromel, J.C., Markov jump linear systems and filtering through network transmitted measurements (2010) Signal Processing, 90, pp. 2842-2850Schenato, L., To Zero or to Hold Control Inputs with Lossy Links (2009) IEEE Transactions on Automatic Control, 54, pp. 1093-1099Sinopoli, B., Schenato, L., Franceschetti, M., Poolla, K., Jordan, M.I., Sastry, S.S., Kalman filtering with intermittent observations (2004) IEEE Transactions on Automatic Control, 49, pp. 1453-1464Wang, Z., Yang, F., Ho, D.W.C., Liu, X., Robust H∞ filtering for stochastic time-delay systems with missing measurements (2006) IEEE Transactions on Signal Processing, 54, pp. 2579-2587Huang, M., Dey, S., Stability of kalman filtering with markovian packet losses (2007) Automatica, 43, pp. 598-607Sahebsara, M., Chen, T., Shah, S.L., Optimal H2 filtering in networked control systems with multiple packet dropout (2007) IEEE Transactions on Automatic Control, 52, pp. 1508-1513Zhang, W.-A., Yu, L., Song, H., H∞ filtering of networked discrete-time systems with (2009) Information Sciences, 179, pp. 3944-3955. , random packet lossesSun, S., Xie, L., Xiao, W., Xiao, N., Optimal filtering for systems with multiple packet dropout (2008) IEEE Transactions on Circuits and Systems, 55, pp. 695-699Seiler, P., Sengupta, R., An H∞ approach to networked control (2005) IEEE Transactions on Automatic Control, 50, pp. 356-364Geromel, J.C., Gonçalves, A.P.C., Fioravanti, A.R., Dynamic output feedback control of discrete-time markov jump linear systems through linear matrix inequalities (2009) SIAM Journal on Control and Optimization, 48, pp. 573-593Hadjicostis, C.N., Touri, R., Feedback control utilizing packet dropping network links (2002) Proc. 41st Conf. Decision and Control, 2, pp. 1205-1210Seiler, P., Sengupta, R., Analysis of communication losses in vehicle control problems (2001) Proc. 2001 Amer. Contr. Conf., 2, pp. 1491-1496Zhang, W., Branicky, M.S., Phillips, S.M., Stability of networked control systems (2001) IEEE Control Systems Magazine, 21, pp. 84-99Schenato, L., Optimal estimation in networked control systems subject to random delay and packet drop (2008) IEEE Transactions on Automatic Control, 53, pp. 1311-1317Smith, S.C., Seiler, P., Estimation with lossy measurements: Jump estimators for jump systems (2003) IEEE Transactions on Automatic Control, 48, pp. 2163-2171Costa, O.L.V., Guerra, S., Stationary filter for linear minimun mean square error estimator of discrete-time markovian jump systems (2002) IEEE Transactions on Automatic Control, 47, pp. 1351-1356Costa, O.L.V., Guerra, S., Robust linear filtering for discrete-time hybrid Markov linear systems (2002) International Journal of Control, 75, pp. 712-727Fioravanti, A.R., Gonçalves, A.P.C., Geromel, J.C., H2 filtering of discrete-time markov jump linear systems through linear matrix inequalities (2008) International Journal of Control, 81, pp. 1221-1231Gonçalves, A.P.C., Fioravanti, A.R., Geromel, J.C., H∞ filtering of discrete-time markov jump linear systems through linear matrix inequalities (2009) IEEE Transactions on Automatic Control, 54, pp. 1347-135