Control systems, driven by a discontinuous unit feedback in a Hilbert space
, are studied. The equation which describes a system motion, taking place i
n the discontinuity manifold and further referred to as a sliding mode, is
derived by means of a special regularization technique, Based on the slidin
g mode equation, the procedure of synthesis of a discontinuous unit control
signal is developed. Restricted to a class of infinite-dimensional systems
with finite-dimensional unstable part, this procedure generates the contro
l law which ensures desired dynamic properties as well as robustness of the
closed-loop system with respect to matched disturbances. As an illustratio
n of the capabilities of the procedure proposed, a scalar unit controller o
f an uncertain exponentially minimum phase dynamic system is constructed an
d applied to heat processes and distributed mechanical oscillators.