This paper develops discontinuous control methods for minimum-phase semilinear infinite-dimensional systems driven in a Hilbert space. Control algorithms presented ensure asymptotic stability, global or local accordingly, as state feedback or output feedback is available, as well as robustness of the closed-loop system against external disturbances with the a priori known norm bounds. The theory is applied to stabilization of chemical processes around prespecified steady-state temperature and concentration profiles corresponding to a desired coolant temperature. Two specific cases, a plug flow reactor and an axial dispersion reactor, governed by hyperbolic and parabolic partial differential equations of first and second order, respectively, are under consideration. To achieve a regional temperature feedback stabilization around the desired profiles, with the region of attraction, containing a prescribed set of interest, a component concentration observer is constructed and included into the closed-loop system so that there is no need for measuring the process component concentration which is normally unavailable in practice. Performance issues of the discontinuous feedback design are illustrated in a simulation study of the plug flow reactor.