]> 3.1 Introduction

3.1 Introduction

The aim of this section is to present an exact method of evaluating the quadratic performance index for infinite–dimensional systems. Our method relies on solving the Lyapunov operator equation with unbounded operators. For delay–differential systems of the neutral type an explicit construction of the solution to the Lyapunov operator equation is given. The results are illustrated by two examples of the determination of a classical controller setting. An approximation method of evaluating the quadratic performance index is also provided and compared with the exact method. Let us consider some examples motivating our investigations.

  3.1.1 Example 1: Nuclear reactor temperature control I
  3.1.2 Example 2: Distortionless RLCG transmission line I
  3.1.3 Example 3: Automatic control system with PID controller