Discontinuous unit feedback control of uncertain infinite-dimensional systems

Control systems, driven by a discontinuous unit feedback in a Hilbert space, are studied. The equation which describes a system motion, taking place in the discontinuity manifold and further referred to as a sliding mode, is derived by means of a special regularization technique. Based on the sliding 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 control law which ensures desired dynamic properties as well as robustness of the closed-loop system with respect to matched disturbances. As an illustration of the capabilities of the procedure proposed, a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators.