Optimal and Robust Control, 2nd Edition

6Reduced Order Models and Symmetric Systems

DOI: 10.1201/9781003196921-6

CONTENTS

• 6.1 Reduced Order Models Based on the Open-loop Balanced Realization

  • 6.1.1 Direct Truncation Method

  • 6.1.2 Singular Perturbation Method

• 6.2 Reduced Order Model Exercises

• 6.3 Symmetric Systems

  • 6.3.1 Reduced Order Models for SISO Systems

  • 6.3.2 Properties of Symmetric Systems

  • 6.3.3 The Cross-gramian Matrix

  • 6.3.4 Relations Between ${\text{W}}_c^2$, ${\text{W}}_o^2$ and ${\text{W}}_{co}$

  • 6.3.5 Open-loop Parameterization

  • 6.3.6 Relation Between the Cauchy Index and the Hankel Matrix

  • 6.3.7 Singular Values for a FIR Filter

  • 6.3.8 Singular Values of All-pass Systems

• 6.4 Exercises

In this chapter we look at constructing a reduced order model from a dynamical system. This represents the practical application ...