An introduction to discontinuous feedback in control

Francis Clarke
Université Claude Bernard Lyon 1



Very few control systems of real interest are linear. Yet, the study of linear systems has been responsible for most of the many important successes of control theory. The explanation of this apparent paradox lies in the widespread use of the technique known as linearization, in which a nonlinear system is approximated by a linear one. This methodology is not always available, however, since linearization can fail for a variety of reasons (degeneracy, state constraints, nonsmoothness...). In such cases, the true underlying nonlinearity must be dealt with, and it turns out that discontinuous feedbacks must be considered. The design and analysis of such feedbacks is a subject that is currently under active development.