In this letter, we investigate the local stability in equilibrium for Internet congestion control algorithm proposed by Low (IEEE/ACMTRANSACTIONS ONNETWORKING, 1999). The network consists of multisource and one-bottleneck link with heterogenous time-varying propagation delays. Linear matrix inequality (LMI) stability criteria is presented for discrete congestion control algorithm of TCP/REM dual model, which can be efficiently and easily solved by the LMI toolbox provided by Matlab software. An important feature is to acquire the maximum network delays to guarantee the stability of congestion control algorithm, i.e., the scale stability domain of REM algorithm. Index Terms-Congestion control, linear matrix inequality (LMI), Local stability, REM.

This paper discusses an adaptive fuzzy controller design method for chaotic systems in the presence of completely unknown nonlinearities and disturbances. All the unknown nonlinear functions are estimated by dynamic fuzzy approximators so that the adaptive fuzzy control approach can be employed in the chaotic systems. Moreover, H∞ control method is applied to attenuate the effect of the modeling errors and disturbances in tracking control. An example is given to illustrate the effectiveness of this approach.

In this note, the problem of control for a class of chaotic systems is studied. Only partial information of the systems states is known. First, an adaptive observer is designed to ensure the corresponding error system asymptotically stable. Then, based on the states obtained by the above observer, a nonlinear state feedback controller is constructed for the chaotic system, which, according to the input to state stable (ISS) principal, guarantees the closed-loop chaotic system is asymptotically stable. A numerical example is included to show the effectiveness of the proposed techniques.

Robust control problem of nonlinear time-delay chaotic systems is investigated. For such uncertain systems, we propose adaptive feedback controller and novel nonlinear feedback controller. They are both independent of the time delay and can render the corresponding closed-loop systems globally uniformly ultimately bounded stable. The simulations on controlling logistic system are made and the results show the controllers are feasible.