Control problem for a parabolic partial differential equation system is discussed. Control problem is to provide desired transient performances in presence of an unknown external distributed disturbance and time-varying parameters. The presented design methodology of continuoustime distributed controller as well as discrete-time distributed controller guarantees desired transients by inducing of twotime-scale motions in the closed-loop system. Stability conditions imposed on the fast and slow

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... des and sufficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop partial differential equation system achieves the desired properties in such a way that the transient performances are desired and insensitive to external distributed disturbance and parameter variations. The method of singular perturbations is used through the paper. 0-7803-9235-3/05/$20.00