The purpose of this chapter is to present some definitions and background theory that will be used throughout this book. We will first introduce some important theorems based on Lyapunov theory. We will give some notions and basic concepts of passivity. Then, we will recall a necessary condition for the existence of a continuously stabilizing control law for non-linear systems, often referred to as Brockett’s necessary condition. The definitions of non-holonomic systems, underactuated systems and a homoclinic orbit are also given.
KeywordsManifold Dition Exter
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