Robustness of network $ow control against disturbances and time-delay
نویسندگان
چکیده
This paper studies robustness of Kelly’s source and link control laws in (J. Oper. Res. Soc. 49 (1998) 237) with respect to disturbances and time-delays. This problem is of practical importance because of unmodelled $ows, and propagation and queueing delays, which are ubiquitous in networks. We ;rst show Lp-stability, for p∈ [1;∞], with respect to additive disturbances. We pursue L∞-stability within the input-to-state stability (ISS) framework of Sontag (IEEE Trans. Automat. Control 34 (1989) 435), which makes explicit the vanishing eAect of initial conditions. Next, using this ISS property and a loop transformation, we prove that global asymptotic stability is preserved for suBciently small time-delays in forward and return channels. For larger delays, we achieve global asymptotic stability by scaling down the control gains as in Paganini et al. (Proceedings of 2001 Conference on Decision and Control, Orlando, FL, December 2001, pp. 185–190) c © 2004 Elsevier B.V. All rights reserved.
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