Two-Dimensional Hybrid Dynamical Systems

Abstract

In this chapter, we focus on the case in which the continuous state space of the multivalued differential automaton is two-dimensional. The general theory developed in Chapter 3 is applied to establish an analog of the classic Poincaré-Bendixon theorem. This theorem states that, for a planar autonomous ordinary differential equation, any trajectory lying in a bounded invariant domain either

• 1) is constant, or

• 2) is periodic, or

• 3) converges to one of no more than countably many equilibrium points, or

• 4) converges to one of no more than countably many limit cycles