M. Rotkowitz
Parameterization of Causal Stabilizing Controllers over Networks with Delays
Proceedings of the IEEE Global Telecommunications Conference, November 2006.

Abstract

We consider the problem of multiple subsystems, each with its own controller, such that the dynamics of each subsystem may affect those of other subsystems with some propagation delays, and the controllers may communicate with each other with some transmission delays. It was recently shown, assuming linearity and time-invariance of the subsystems and their controllers, that if the transmission delays satisfy the triangle inequality, then the simple condition that the transmission delay between any two subsystems is less than the propagation delay between those subsystems allows for the optimal control problem to be recast as a convex optimization problem. In this paper it is shown that the same condition allows for parameterization of all causal stabilizing decentralized controllers, even if the subsystems or admissible controllers are nonlinear time-varying.