**Chapter 4Review of Stability Theory Applied to The Transient Energy Function Method**

**4.1 Introduction**

**4.1.1 Notational Conventions**

We will first provide a brief description of the notational convention used in this chapter.

*x ∈ A*
| means *x* is an element of the set *A* |

*x**A*
| means *x* is not an element of the set *A* |

*R*
| is the set of all real numbers |

*R × R*
| denotes the Cartesian product, i.e., if *x*, *y ∈ R*, the ordered pair (*x, y*) *∈ R × R* |

*R*^{n}
| is the *n*–dimensional real space |

· | is an appropriately defined norm |

*B*_{r}
| ball of radius *r, r > o*, and centered at the origin |