Benchmark Models

Abstract

This chapter previews discontinuous models which arise in the sequel. Section 1.1 conceptually introduces variable structure systems, generating first- and higher-order sliding modes in continuous- and discrete-time perspectives. In addition, the so-called chattering phenomenon is discussed, and sliding mode dynamics are exemplified in the infinite-dimensional setting. Section 1.2 involves into consideration of unilateral constraints and features specific modes such as state resets, Zeno behavior, and Hopf bifurcation which may occur because of the constraints. While dealing with a certain impact dynamics, the Zhuravlev–Ivanov transformation is additionally involved for avoiding the state resets of the transformed vector field which turns out to be discontinuous (rather than impulsive), even if the original field is continuous.