Introduction

Abstract

In many systems the physical quantity of interest depends on several independent variables. For instance, the temperature of an object depends on both position and time, as do structural vibrations and the temperature and velocity of water in a lake. When the dynamics are affected by more than one independent variable, the equation modeling the dynamics involves partial derivatives and is thus a partial differential equation (PDE). Since the solution of the PDE is a physical quantity, such as temperature, that is distributed in space, these systems are often called distributed parameter systems (DPS). The state of a system modeled by an ordinary differential equation evolves on a finite-dimensional vector space, such as $${\mathbb R}^n.$$ In contrast, the solution to a partial differential equation evolves on an infinite-dimensional space. For this reason, these systems are often called infinite-dimensional systems. The underlying distributed nature of the physical problem affects the dynamics and controller design.