Model Reduction Techniques using Interval Analysis and Optimization

Existing model reduction techniques for lower
order controller design have certain limitations in
terms of their applicability, reliability and
accuracy. The main objective of this book is to
present new tools that overcome these limitations
for a large class of linear time invariant fixed and
interval systems. This book presents two fold
contributions for control system design problem.
First, the improved model order reduction methods
are described for linear time invariant fixed
and interval systems. Second, suppose a reduced
order controller is designed from the reduced order
model for the original higher order system, it does
not guarantee the stability of the resulting closed
loop system. Thus, the problem of stabilization of
the original system when controller is designed
from the reduced order model is addressed using the
theory of passivity. Theoretical results concerning
key properties of the described techniques such as
stability, accuracy are derived. The proposed
methods are demonstrated on several difficult
examples, including those that can not be readily
solved by the existing techniques.