Introduction

Abstract

Dynamical systems are systems that evolve with respect to time. They represent the overwhelming majority of systems. The objective of scientists is first to model them as accurately as possible in order to have optimal knowledge of their evolution and to design controls of the evolution in order to accomplish certain objectives. A significant evolution in the modeling and theory of dynamical systems occurred in the late 1950s and early 1960s, resulting in what is called the modern theory of dynamical systems and control theory. A key element is the state representation of dynamical systems, also called the internal representation. Previously, dynamical systems were modeled by an external representation, also called an input–output relation.