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Stabilization of Markov jump linear systems using quantized state feedback. (English) Zbl 1204.93127
Summary: This paper addresses the stabilization problem for single-input Markov jump linear systems via mode-dependent quantized state feedback. Given a measure of quantization coarseness, a mode-dependent logarithmic quantizer and a mode-dependent linear state feedback law can achieve optimal coarseness for mean square quadratic stabilization of a Markov jump linear system, similar to existing results for linear time-invariant systems. The sector bound approach is shown to be non-conservative in investigating the corresponding quantized state feedback problem, and then a method of optimal quantizer/controller design in terms of linear matrix inequalities is presented. Moreover, when the mode process is not observed by the controller and quantizer, a mode estimation algorithm obtained by maximizing a certain probability criterion is given. Finally, an application to networked control systems further demonstrates the usefulness of the results.

93E15Stochastic stability
93C05Linear control systems
93D15Stabilization of systems by feedback
60J75Jump processes
93B52Feedback control
Full Text: DOI
[1] Boukas, E.; Liu, Z.: Robust H$\infty $control of discrete-time Markovian jump linear systems with mode-dependent time-delays, IEEE transactions on automatic control 46, No. 12, 1918-1924 (2001) · Zbl 1005.93050 · doi:10.1109/9.975476
[2] Costa, O.; Fragoso, M.; Marques, R.: Discrete-time Markov jump linear systems, (2005) · Zbl 1081.93001
[3] De Souza, C.: Robust stability and stabilization of uncertain discrete-time Markovian jump linear systems, IEEE transactions on automatic control 51, No. 5, 836-841 (2006)
[4] Elia, N.: Remote stabilization over fading channels, Systems and control letters 54, No. 3, 237-249 (2005) · Zbl 1129.93498 · doi:10.1016/j.sysconle.2004.08.009
[5] Elia, N.; Mitter, S.: Stabilization of linear systems with limited information, IEEE transactions on automatic control 46, No. 9, 1384-1400 (2001) · Zbl 1059.93521 · doi:10.1109/9.948466 · http://ieeexplore.ieee.org/search/wrapper.jsp?arnumber=948466
[6] Elliott, R.; Aggoun, L.; Moore, J.: Hidden Markov models estimation and control, (1995) · Zbl 0819.60045
[7] Elliott, R.; Dufour, F.; Malcolm, W.: State and mode estimation for discrete-time jump Markov systems, SIAM journal on control and optimization 44, 1081-1104 (2005) · Zbl 1130.93423 · doi:10.1137/S0363012904442628
[8] Fu, M.; Xie, L.: The sector bound approach to quantized feedback control, IEEE transactions on automatic control 50, No. 11, 1698-1711 (2005)
[9] Gao, H.; Chen, T.: A new approach to quantized feedback control systems, Automatica 44, No. 2, 534-542 (2008) · Zbl 1283.93131
[10] Ho, T.; Chen, B.: Novel extended viterbi-based multiple-model algorithms for state estimation of discrete-time systems with Markov jump parameters, IEEE transactions on signal processing 54, No. 2, 393-404 (2006)
[11] Hoshina, H., Tsumura, K., & Ishii, H. (2007). The coarsest logarithmic quantizers for stabilization of linear systems with packet losses. In Proceedings of the 46th IEEE conference on decision and control. (pp. 2235--2240) New Orleans, USA.
[12] Huang, M.; Dey, S.: Stability of Kalman filtering with Markovian packet losses, Automatica 43, No. 4, 598-607 (2007) · Zbl 1261.93083
[13] Hu, S.; Yan, W.: Stability robustness of networked control systems with respect to packet loss, Automatica 43, No. 7, 1243-1248 (2007) · Zbl 1123.93075 · doi:10.1016/j.automatica.2006.12.020
[14] Imer, O.; Yüksel, S.; Başar, T.: Optimal control of LTI systems over unreliable communication links, Automatica 42, No. 9, 1429-1439 (2006) · Zbl 1128.93368 · doi:10.1016/j.automatica.2006.03.011
[15] Matei, I., Martins, N., & Baras, J. (2008). Optimal linear quadratic regulator for Markovian jump linear systems, in the presence of one time-step delayed mode observations, In Proceedings of the 17th IFAC world congress. (pp. 8056--8061) Seoul, Korea.
[16] Rabiner, L.: A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE 77, No. 2, 257-286 (1989)
[17] Schenato, L.; Sinopoli, B.; Franceschetti, M.; Poolla, K.; Sastry, S.: Foundations of control and estimation over lossy networks, Proceedings of the IEEE 95, No. 1, 163-187 (2007)
[18] Seiler, P.; Sengupta, R.: An H$\infty $approach to networked control, IEEE transactions on automatic control 50, No. 3, 356-364 (2005)
[19] Sinopoli, B.; Schenato, L.; Franceschetti, M.; Poolla, K.; Jordan, M.; Sastry, S.: Kalman filtering with intermittent observations, IEEE transactions on automatic control 49, No. 9, 1453-1464 (2004)
[20] Viterbi, A.: Error bounds for convolutional codes and an asymptotically optimum decoding algorithm, IEEE transactions on information theory 13, No. 2, 260-269 (1967) · Zbl 0148.40501 · doi:10.1109/TIT.1967.1054010
[21] Xiao, N., Xie, L., & Fu, M. (2009). Quantized stabilization of Markov jump linear systems via state feedback. In Proceedings of American control conference. (pp. 4020--4025), St. Louis, USA.
[22] Xiong, J.; Lam, J.: Stabilization of linear systems over networks with bounded packet loss, Automatica 43, No. 1, 80-87 (2007) · Zbl 1140.93383 · doi:10.1016/j.automatica.2006.07.017