The sliding mode control problem for distributed parameter systems (DP
S) is studied. Two mathematical description theorems of sliding modes
are obtained using a novel analysis approach. The existence conditions
of sliding modes are proposed for general DPS; and the sliding mode (
SM) controllers are also designed straightforwardly for a class of DPS
. An important feature of the theory is that the system is made insens
itive to system uncertainties once the sliding manifold is reached.