Finite-dimensional Filippov method for infinite-dimensional SMC system

The paper deals with a well-posedness analysis for discontinuous infinite-dimensional systems, which can be regularized by means of the conventional (finite-dimensional) Filippov method. The study is inspired by sliding mode control theory. Sliding mode controllers for infinite-dimensional systems with finite- and infinite-dimensional sliding surfaces are designed. Theoretical results are supported by an example of an output-based sliding mode control for heat system.