The H {Infinity} Control Problem
A State Space Approach
A.A. Stoorvogel(Author)
Prentice-Hall (Publisher)
Published on 1. January 1992
Book
Hardback
468 pages
978-0-13-388067-0 (ISBN)
Description
The infinity norm as a measure has been thoroughly embedded in control theory during the last few years. Although the infinity norm has been used in control for a long time (a concept like bounded real is nothing else than an infinity norm bound), there was a gigantic surge in research efforts towards the minimization of the infinity norm of the closed loop system in the last 10 years. A fairly complete solution is now available. This book tries to bring the reader up to date with respect to the state space approach to the infinity control problem. This book contains numerous references towards other approaches to this theory which the reader can use as a starting point for further research. The book starts at a basic level with the prerequisites being graduate level courses on linear algebra and state space systems. On the other hand, it includes the most general solutions available at the time this book was written.
More details
Series
Language
English
Place of publication
Harlow
United Kingdom
Publishing group
Pearson Education Limited
Target group
College/higher education
Professional and scholarly
Illustrations
bibliography, index
Dimensions
Height: 236 mm
Width: 152 mm
Weight
468 gr
ISBN-13
978-0-13-388067-0 (9780133880670)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Person
Author
Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, USA
Content
Part 1 Introduction: robustness analysis; the infinity control problem; stabilization of uncertain systems; the graph topology; the mixed-sensitivity problem; main items of this book - singular systems, differential game, the minimum entropy infinity control problem, the finite horizon infinity control problem, discrete time systems. Part 2 Notation and basic properties: introduction; linear systems - continuous time, discrete time; rational matrices; geometric theory; the Hardy and Lebesgues spaces - continuous time, discrete time; (almost) disturbance decoupling problems. Part 3 The regular full-information infinity control problem: introduction; problem formulation and main results; intuition for the formal proof; solvability of the Riccati equation; existence of a suitable controller. Part 4 The general full-information infinity control problem: introduction; problem formulation and main results; solvability of the quadratic matrix inequality; existence of state feedback laws; the design of a suitable compensator; a direct feed through matrix from disturbance to output; invariant zeros on the imaginary axis - frequency domain loop shifting, cheap control; conclusion. Part 5 The infinity control problem with measurement feedback: introduction; problem formulation and main results; reduction of the original problem to an almost disturbance decoupling problem; the design of a suitable compensator; characterization of achievable closed loop systems; no assumptions on any direct feedthrough matrix - an extra direct-feedthrough matrix from disturbance to output, an extra direct-feedthrough matrix from control to measurement; conclusion. Part 6 The singular zero-sum differential game with stability: introduction; problem formulation and main results; existence of almost equilibria; necessary conditions for the existence of almost equilibria; the regular differential game; conclusions. Part 7 The singular minimum entropy infinity control problem: introduction; problem formulation and results; properties of the entropy function; a system transformation; (almost) disturbance decoupling and minimum entropy; conclusion. Part 8 The finite horizon finite control problem: introduction; problem formualtion and main results; completion of the squares; existence of compensators; concluding remarks.