ABSTRACT
This chapter aims to develop effective methods for determining the existence and stability properties of periodic orbits in nonlinear systems with impulse effects. It shows that the methods are systematic, broadly applicable, and practical in terms of computations. The chapter examines method of Poincare sections augmented with notions of timescale decomposition, invariance, and attractivity in order to simplify its application to complex systems, while maintaining analytical rigor. It addresses how to formally include discrete control actions in the stability analysis. The classical technique for determining the existence and stability properties of periodic orbits in nonlinear systems involves Poincare sections and Poincare return maps. The Poincare return map transforms the problem of finding periodic orbits into one of finding fixed points of a map, which in turn can be viewed as the problem of finding equilibrium points of a particular discrete-time nonlinear system.
