On modeling, analysis and design of piecewise linear control systems

Piecewise linear systems have a broad applicability in a wide range of engineering sciences: systems operating in different modes or subject to physical constraints are naturally modelled as piecewise linear; some of the most common nonlinearities in control systems, such as relays and saturations, are piecewise linear; etc. Although analyses of specific piecewise linear systems appeared already in the late 1800s, it is fair to say that the circuits and systems community was the first to recognize piecewise linear systems as an interesting system class in its own right. Demanding applications, a shortage of techniques for dealing with hybrid systems and the emergence of new computational tools has now sparked a strong interest for piecewise linear systems also in the control community. The purpose of this paper is to provide a short overview of some recent results in this field.