Stability and Asymptotic Behaviour of Nonlinear Systems: an Introduction

To motivate a study of asymptotic behaviour of nonlinear systems modelled by ordinary differential equations and differential inclusions, we indicate how such equations/inclusions arise naturally in control of dynamical process by feedback. The concept of control pertains to modifying the behaviour of the process, by manipulation of inputs to the process, in order to achieve some prescribed goal. Fundamental to this is the notion of feedback: a strategy in which the inputs to the process are determined on the basis of concurrent observations on (or outputs from) the process.