Robust control and filtering of singular systems. (English) Zbl 1114.93005
Lecture Notes in Control and Information Sciences 332 (ISBN 3-540-32797-5/pbk). xii, 234 p. (2006).
For some physical system it is preferable to choose a nonminimal set of descriptor variables for developing a mathematical model. This may result in singular system models. Such systems are investigated in this book. In the main part of the book results on robustness analysis, robust control and filtering for uncertain systems are presented.
The book is divided into 10 chapters. Continuous systems and discrete systems are investigated in parallel throughout the book.
After a short introduction some basic definitions such as regularity, nonimpulsiveness or causality and stabilitity are given in the second chapter.
Stabilizing controller design for singular systems is investigated in chapter 3. The problem is reduced to the solution of linear matrix inequalities (LMI).
The proposed methods are extended for robust stabilization in chapter 4. The notion of generalized quadratic stability is introduced. Expressions for robustly stabilizing state feedback controllers are presented.
In chapter 5 the \(H_\infty\) approach for uncertain singular systems is studied.
The guaranteed cost control problem for linear singular systems is considered in chapter 6. State feedback controller for quadratic performance indicts are developed.
Chapter 7 is devoted to positive real control. It is shown that feedback controllers can be constructed by solving matrix inequalities.
The filtering problem for singular systems is studied in chapter 8. Instead of a Kalman filter the \(H_\infty\) approach is proposed. Again linear matrix inequalities must be solved. In chapter 9 control and filtering problems for singular systems with time delays are investigated.
In the last chapter Markovian jump singular systems are studied. Markovian jump systems are used to model stochastic systems with abrupt structure variations. Stability analysis and the \(H_\infty\) control problem are investigated.
The \(H_\infty\) approach plays a central role in this book. The proposed analysis and design methods are heavely based on solving linear matrix equality systems. The book gives a mathematically well founded presentation of analysis and design methods for singular systems.
The book is divided into 10 chapters. Continuous systems and discrete systems are investigated in parallel throughout the book.
After a short introduction some basic definitions such as regularity, nonimpulsiveness or causality and stabilitity are given in the second chapter.
Stabilizing controller design for singular systems is investigated in chapter 3. The problem is reduced to the solution of linear matrix inequalities (LMI).
The proposed methods are extended for robust stabilization in chapter 4. The notion of generalized quadratic stability is introduced. Expressions for robustly stabilizing state feedback controllers are presented.
In chapter 5 the \(H_\infty\) approach for uncertain singular systems is studied.
The guaranteed cost control problem for linear singular systems is considered in chapter 6. State feedback controller for quadratic performance indicts are developed.
Chapter 7 is devoted to positive real control. It is shown that feedback controllers can be constructed by solving matrix inequalities.
The filtering problem for singular systems is studied in chapter 8. Instead of a Kalman filter the \(H_\infty\) approach is proposed. Again linear matrix inequalities must be solved. In chapter 9 control and filtering problems for singular systems with time delays are investigated.
In the last chapter Markovian jump singular systems are studied. Markovian jump systems are used to model stochastic systems with abrupt structure variations. Stability analysis and the \(H_\infty\) control problem are investigated.
The \(H_\infty\) approach plays a central role in this book. The proposed analysis and design methods are heavely based on solving linear matrix equality systems. The book gives a mathematically well founded presentation of analysis and design methods for singular systems.
Reviewer: Rudolf Tracht (Essen)
MSC:
| 93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |
| 93D09 | Robust stability |
| 93E11 | Filtering in stochastic control theory |
| 93B36 | \(H^\infty\)-control |
