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Model Reduction Techniques using Interval Analysis and Optimization
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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.
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