Stability of discrete-time systems with time-varying delays

Congestion control and the associated issue of stability of communication networks have attracted considerable attention recently. The resulting problems are extremely difficult to solve due to the presence of several sources of time-varying delays. Due mainly to the fact that the ensuing models are non-trivial, most existing work relies on simplified piecewise time-invariant models to describe these network delays. This however may not capture important aspects of network behavior especially when dealing with high-speed networks. Study of such networks requires a better understanding of the dynamics of time-varying delays encountered in discrete-time systems. In this paper, we identify and propose the models for two distinctly different types of such delays. These models can accommodate network and application-specific delay variations; their flexibility is demonstrated in a distributed sensor network setting. A stability result that accounts for time-varying delays and nonlinearities of the type one typically encounters in high-speed communication networks is also presented.