H∞ Control of Linear Systems with Multiple Input Delays with Application to ATM Network Congestion Control

This paper is concerned with the finite horizon H
_infin
control problem for discrete time systems with multiple input delays. We extend the existing work (Zhang et al., 2005) by allowing a more general form of controlled output. A linkage between the H
_infin
control problem and a smoothing problem is first established which allows us to give a sufficient solvability condition for the H
_infin
control problem by classical estimation theory. Our solution is given in terms of one Riccati difference equation of the same dimension of the plant (ignoring the delays). As a special case, a complete solution to the H
₂
state feedback control of systems with multiple input delays is derived. The H
_infin
control result is then applied to ATM congestion control. Simulations show that the proposed control technique can achieve desired control performance very efficiently and is robust to the varying round trip delay of the ATM network to some extent