A strong and growing theme in the design and analysis of network control systems is to state the control objectives in terms of optimisation theory, and then to present the network dynamics (or protocol behaviour) as a process that seeks a solution of this optimisation problem. Flow control algorithms, including TCP, have been extensively analysed through various utility maximisation problems, as has power control in mobile radio systems.
We present a stability result for a class of dynamic processes that find the saddle point of a Lagrangian, including Lagrangians derived from optimisation problems. Our formulation is symmetric in primal and dual variables, and automatically derives a Lyapunov function from the form of the dynamic equations. We show how several stability results from the literature of distributed flow control in networks fit into this formalism.