Control of parabolic distributed systems with delay in feedback loop

The problem of regulation with guaranteed transient performances for parabolic distributed systems with delayed control is discussed. The representation of the parabolic distributed system by infinite-dimensional system of differential equations is used. The fast infinite-dimensional controller with the highest output derivative in feedback loop is introduced and hence, two-time-scale motions are induced in the closed-loop system. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate can ensure that the full-order closed-loop system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and parameter variations in the system. Constraint set for selection of the controller parameters caused by delay is considered.