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.