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Remote stabilization over fading channels. (English) Zbl 1129.93498

Summary: We study the problem of remote mean square stabilization of a MIMO system when independent fading channels are dedicated to each actuator and sensor. We show that the stochastic variables responsible for the fading can be seen as a source of model uncertainty. This view leads to robust control analysis and synthesis problems with a deterministic nominal system and a stochastic, structured, model uncertainty. As a special case, we consider the stabilization over Erasure or drop-out channels. We show that the largest probability of erasure tolerable by the closed loop is obtained from solving a robust control synthesis problem. In more general terms, we establish that the set of plants which can be stabilized by linear controllers over fading channels is fundamentally limited by the channel generated uncertainty. We show that, the notion of mean square capacity, defined for a single channel in the loop, captures this limitation precisely and characterizes equivalence classes of channels within the class of memoryless fading channels.

MSC:

93D15 Stabilization of systems by feedback
90B18 Communication networks in operations research
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[2] Costa, O.; Fragoso, M., Stability results for discrete-time linear systems with Markovian jumping parameters, J. Math. Anal. Appl., 179, 154-178 (1993) · Zbl 0790.93108
[3] Dullerud, G. E.; Paganini, F., A Course in Robust Control TheoryA Convex Approach (2000), Springer: Springer New York
[4] El Bouhtouri, A.; Hinrichsen, D.; Pritchard, A. J., Stability radii of discrete-time stochastic systems with respect to blockdiagonal perturbations, Automatica, 36, 7, 1033-1040 (2000) · Zbl 0961.93042
[6] Elia, N., Stabilization of systems with erasure actuation and sensory channels, (Proceedings of the 40th Allerton Conference on Communication, Control, and Computing (2002))
[10] Gahinet, P.; Apkarian, P., A linear matrix inequality approach to \(H_\infty\) control, Internat. J. Nonlinear Robust Control, 4, 421-448 (1994) · Zbl 0808.93024
[14] Horn, R.; Johnson, C., Matrix Analysis (1985), Cambridge University Press: Cambridge University Press Cambridge, MA · Zbl 0576.15001
[15] Khammash, M.; Salapaka, M. V.; Van Voorhis, T., Robust synthesis in \(\ell_1\): a globally optimal solution, IEEE Trans. Automat. Control, 46, 11, 1744-1754 (2001) · Zbl 1038.93031
[16] Kleinman, D. L., Optimal stationary control of linear systems with control-dependent noise, IEEE Trans. Automat. Control, 14, 673-677 (1969)
[17] Ku, R. T.; Athans, M., Further results on the uncertainty threshold principle, IEEE Trans. Automat. Control, 22, 5, 866-868 (1977) · Zbl 0366.93042
[19] Lu, Jianho; Skelton, R. E., Mean-square small gain theorem for stochastic controldiscrete-time case, IEEE Trans. Automat. Control, 47, 3, 490-494 (2002) · Zbl 1364.93867
[23] Scherer, C.; Gahinet, P.; Chitali, M., Multiobjective output-feedback control via LMI optimization, IEEE Trans. Automat. Control, 42, 7, 896-911 (1997) · Zbl 0883.93024
[24] Seiler, P.; Sengupta, R., Analysis of communication losses in vehicle control problems, (Proceedings of IEEE American Control of Conference (2001)), 1491-1496
[29] Willems, J. C.; Blankenship, G. L., Frequency domain stability criteria for stochastic systems, IEEE Trans. Automat. Control, 16, 4, 292-299 (1971)
[30] Shing Wong, Wing; Brockett, R. W., Systems with finite communication bandwidth constraints. II. Stabilization with limited information feedback, IEEE Trans. Automat. Control, 44, 5, 1049-1053 (1999) · Zbl 1136.93429
[31] Wonham, W. M., Optimal stationary control of linear systems with state-dependent noise, SIAM J. Control Optim., 5, 486-500 (1967) · Zbl 0218.49003
[32] Zhang, Mingjun; Tarn, Tzyh-Jong, Hybrid control of the Pendubot, IEEE/ASME Trans. Mechatronics, 7, 1, 79-86 (2002)
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