We address the global asymptotic stability of FAST TCP, especially considering cross traffics, time-varying network feedback delay, and queuing delay dynamics at link. Exploiting the inherent dynamic property of FAST TCP, we construct two sequences that represent the lower and upper bound variations of the congestion window in time. By showing that the sequences converge to the equilibrium point of the congestion window, we establish that FAST TCP in itself is globally asymptotically stable without any specific conditions on the tuning parameter α or the update gain γ.

We consider a single-link multi-source network with FAST TCP sources. We adopt a continuous-time dynamic model for FAST TCP sources, and propose a static model to adequately describe the queuing delay dynamics at the link. The proposed model turns out to have a structure that reveals the time-varying network feedback delay, which allows us to analyze FAST TCP with due consideration of the time-varying network feedback delay. Based on the proposed model, we establish sufficient conditions for the boundedness of congestion window of each source and for the global asymptotic stability. The asymptotic stability condition shows that the stability property of each source is affected by all other sources sharing the link. Simulation results illustrate the validity of the sufficient condition for the global asymptotic stability.

We consider a class of nonlinear time delay systems with time-varying delays, and achieve a time delay independent sufficient condition for the global asymptotic stability. The sufficient condition is proved by constructing a continued fraction that represents the lower and upper bound variations of the system trajectory along the current of time, and showing that the continued fraction converges to the equilibrium point of the system. The simulation results show the validity of the sufficient condition, and illustrate that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for the global asymptotic stability.

Recurrent neural networks have the potential of performing parallel computation for associative memory and optimization, which is realized by the electronic implementation of neural networks in VLSI technology. Since the time delays in real electronic implementation of neural networks are unavoidably encountered and they can cause systems to oscillate, it is thus practically important to investigate the qualitative properties of neural networks with time delays. In this paper, a class of sufficient conditions is obtained, under which neural networks are globally asymptotically stable independent of time delays.

This paper obtains some new results about the existence, uniqueness, and global asymptotic stability of the equilibrium of a nonlinear continuous neural network, under a sufficient condition weaker than ones presented in the literature. The avobe obtained results can also imply the existing ones about avsolute stability of nonlinear continuous neural networks