Introduction

This book will discuss the stability and controllability of a discrete dynamical system. It is assumed that at any particular time the system can be completely described by a finite dimensional vector xεRm--the state vector. Here Rm is the real m-dimensional Euclidean space and $$x\left\{ {\begin{array}{*{20}{c}} {{{x}_{1}}} \\ \vdots \\ {{{x}_{m}}} \\ \end{array} } \right\} \in R,\left| {\left| x \right|} \right| = {{\left( {x_{1}^{2} + \ldots + x_{m}^{2}} \right)}^{{1/2}}}$$ (the Euclidean length of the vector x). The components x₁,…,x_m might be the temperature, density, pressure etc. of some physical system.