A PI-controller for distributed delay systems (Q1092854)

A finite dimensional control theory is developed for the design of a proportional plus integral control law for tracking step command inputs in general autonomous time-lag systems with distributed heredity in state, control and output variables. With respect to an ordinary differential equation describing the delay system unstable modes, an auxiliary tracking problem is posed. This auxiliary problem derives its importance from the fact that its solution directly yields a solution to the original tracking problem. This point of contact with a finite dimensional system permits the application of well-tested ordinary systems tracking theory to the tracking problem in time-lag systems.