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Analysis and Design of Descriptor Linear Systems [Kõva köide]

  • Formaat: Hardback, 496 pages, kõrgus x laius: 235x155 mm, kaal: 1980 g, XX, 496 p., 1 Hardback
  • Sari: Advances in Mechanics and Mathematics 23
  • Ilmumisaeg: 23-Sep-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1441963960
  • ISBN-13: 9781441963963
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Analysis and Design of Descriptor Linear SystemsSuurem pilt
  • Formaat: Hardback, 496 pages, kõrgus x laius: 235x155 mm, kaal: 1980 g, XX, 496 p., 1 Hardback
  • Sari: Advances in Mechanics and Mathematics 23
  • Ilmumisaeg: 23-Sep-2010
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 1441963960
  • ISBN-13: 9781441963963
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781441963963.html
Märksõnad:
Descriptor linear systems theory is an important part in the general field of control systems theory, and has attracted much attention in the last two decades. In spite of the fact that descriptor linear systems theory has been a topic very rich in content, there have been only a few books on this topic. This book provides a systematic introduction to the theory of continuous-time descriptor linear systems and aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory.The clear representation of materials and a large number of examples make this book easy to understand by a large audience. General readers will find in this book a comprehensive introduction to the theory of descriptive linear systems. Researchers will find a comprehensive description of the most recent results in this theory and students will find a good introduction to some important problems in linear systems theory.

This well structured book provides a systematic introduction to the theory of continuous-time descriptor linear systems. It aims to provide a relatively systematic introduction to the basic results in descriptor linear systems theory.

Arvustused

From the reviews:

This book deals with the analysis and design of descriptor linear systems, which are no doubt of interest to practitioners and theoreticians. The authors present 11 chapters on continuous-time descriptor linear systems. They cite 319 representative references related to the main topics of descriptor systems. All chapters end with some notes and references, useful for the readers understanding of this book, which contains almost 500 pages. This book ends with three useful appendices, which detail some basic mathematical results. (Marco Henrique Terra, Mathematical Reviews, Issue 2011 m)

Preface vii
List of Notation
xvii
1 Introduction
1(34)
1.1 Models for Descriptor Systems
1(4)
1.1.1 State Space Representation
1(2)
1.1.2 Time-Invariant Descriptor Linear Systems
3(2)
1.2 Examples of Descriptor Linear Systems
5(13)
1.2.1 Electrical Circuit Systems
5(2)
1.2.2 Large-Scale Systems with Interconnections
7(1)
1.2.3 Constrained Mechanical Systems
8(4)
1.2.4 Robotic System-A Three-Link Planar Manipulator
12(6)
1.3 Problems for Descriptor Linear Systems Analysis and Design
18(10)
1.3.1 Feedback in Descriptor Linear Systems
18(4)
1.3.2 Problems for Descriptor Linear Systems Analysis
22(2)
1.3.3 Problems for Descriptor Linear Systems Design
24(4)
1.4 Overview of the Book
28(1)
1.5 Notes and References
29(6)
Part I Descriptor Linear Systems Analysis
2 Equivalence and Solutions of Descriptor Linear Systems
35(22)
2.1 Restricted System Equivalence
35(5)
2.1.1 The Definition
36(2)
2.1.2 Common Properties
38(2)
2.2 Canonical Equivalent Forms
40(10)
2.2.1 Dynamics Decomposition Form
40(3)
2.2.2 The Kronecker Form
43(1)
2.2.3 Canonical Equivalent Forms for Derivative Feedback
44(6)
2.3 Solutions of Descriptor Linear Systems
50(5)
2.3.1 System Decomposition Based on the Kronecker Form
50(1)
2.3.2 Solution to the Basic Types of Equations
51(4)
2.4 Notes and References
55(2)
3 Regular Descriptor Linear Systems
57(64)
3.1 Regularity of Descriptor Linear Systems
57(7)
3.1.1 The Definition and Its Relation with Solutions
57(4)
3.1.2 Criteria for Regularity
61(3)
3.2 Equivalence of Regular Descriptor Linear Systems
64(8)
3.2.1 Standard Decomposition Form
65(5)
3.2.2 The Inverse Form
70(2)
3.3 Transfer Function Matrices
72(3)
3.3.1 The Definition
73(1)
3.3.2 Properties
74(1)
3.4 State Responses of Regular Descriptor Linear Systems: Distributional Solutions
75(8)
3.4.1 Solutions of Slow and Fast Subsystems
76(4)
3.4.2 The Distributional Solutions
80(1)
3.4.3 Examples
81(2)
3.5 State Responses of Regular Descriptor Linear Systems: Classical Solutions
83(6)
3.5.1 Consistency
84(1)
3.5.2 The Classical Solutions
85(3)
3.5.3 The Example
88(1)
3.6 Generalized Eigenvalues and Eigenvectors
89(9)
3.6.1 Finite Eigenvalues and Eigenvectors
90(5)
3.6.2 Infinite Eigenvalues and Eigenvectors
95(3)
3.7 Eigenstructure Decomposition with Relation to Standard Decomposition
98(9)
3.7.1 Eigenstructure Decomposition
98(4)
3.7.2 Relation with Standard Decomposition
102(1)
3.7.3 The Deflating Subspaces
103(4)
3.8 Stability
107(6)
3.8.1 The Definition
107(1)
3.8.2 The Direct Criterion
108(2)
3.8.3 Criterion via Lyapunov Equation
110(1)
3.8.4 Examples
111(2)
3.9 Admissibility: Stability plus Impulse-Freeness
113(4)
3.9.1 The Definition
113(1)
3.9.2 The Criterion
114(3)
3.9.3 The Example
117(1)
3.10 Notes and References
117(4)
4 Controllability and Observability
121(78)
4.1 State Reachable Subsets
121(10)
4.1.1 The Definition
122(2)
4.1.2 Characterization of Rt [ 0] and Rt
124(6)
4.1.3 Two Examples
130(1)
4.2 Controllability
131(11)
4.2.1 C-Controllability
132(3)
4.2.2 R-Controllability
135(1)
4.2.3 I-Controllability and S-Controllability
136(6)
4.3 Observability
142(11)
4.3.1 C-Observability
143(4)
4.3.2 R-Observability
147(1)
4.3.3 I-Observability and S-Observability
148(5)
4.4 The Dual Principle
153(3)
4.4.1 The Dual System
153(1)
4.4.2 The Dual Principle
154(2)
4.5 Direct Criteria
156(9)
4.5.1 C-Controllability and C-Observability
157(3)
4.5.2 R-Controllability and R-Observability
160(1)
4.5.3 I-Controllability and I-Observability
161(4)
4.5.4 S-Controllability and S-Observability
165(1)
4.6 Criteria Based on Equivalent Forms
165(12)
4.6.1 Criteria Based on the Dynamics Decomposition Form
165(3)
4.6.2 Criteria Based on the Inverse Form
168(5)
4.6.3 Criteria Based on Equivalent Form for Derivative Feedback
173(4)
4.7 System Decomposition
177(8)
4.7.1 The General Structural Decomposition
178(3)
4.7.2 Special Cases
181(4)
4.8 Transfer Function Matrix and Minimal Realization
185(9)
4.8.1 Transfer Function Matrix
185(2)
4.8.2 Minimal Realization
187(7)
4.9 Notes and References
194(5)
Part II Descriptor Linear Systems Design
5 Regularization of Descriptor Linear Systems
199(28)
5.1 Regularizability under P- (D-) Feedback
199(8)
5.1.1 Proportional Feedback
199(4)
5.1.2 Derivative Feedback
203(4)
5.2 Regularizability under P-D Feedback
207(5)
5.2.1 Problem Formulation
207(2)
5.2.2 Regularizability Conditions
209(3)
5.3 Regularizing Controllers
212(6)
5.3.1 Problem Formulation
212(1)
5.3.2 Preliminaries
213(1)
5.3.3 The Conclusion
214(4)
5.4 Proof of Theorem 5.7
218(6)
5.4.1 Preliminary Results
218(2)
5.4.2 Proof of Theorem 5.7
220(4)
5.5 Notes and References
224(3)
6 Dynamical Order Assignment and Normalization
227(38)
6.1 Assignable Dynamical Orders
227(8)
6.1.1 Full-State Derivative Feedback
228(4)
6.1.2 Partial-State Derivative Feedback
232(3)
6.2 Dynamical Order Assignment via Full-State Derivative Feedback
235(5)
6.2.1 Problem Formulation
236(1)
6.2.2 Preliminary Results
237(1)
6.2.3 Solution to the Problem
238(2)
6.3 Dynamical Order Assignment via State Derivative Feedback with Minimum Norm
240(7)
6.3.1 Problem Formulation
240(1)
6.3.2 A Preliminary Result
241(2)
6.3.3 Solution to the Problem
243(4)
6.4 Dynamical Order Assignment via Partial-State Derivative Feedback
247(9)
6.4.1 Problem Formulation
247(1)
6.4.2 Preliminary Results
248(3)
6.4.3 Solution to the Problem
251(3)
6.4.4 The Example
254(2)
6.5 Normalization of Descriptor Linear Systems
256(6)
6.5.1 Normalizability
256(3)
6.5.2 Normalizing Controllers
259(3)
6.6 Notes and References
262(3)
7 Impulse Elimination
265(40)
7.1 The Impulse-Free Property
265(7)
7.1.1 Basic Criteria
266(2)
7.1.2 Criteria Based on Equivalent Forms
268(4)
7.2 Impulse Elimination by State Feedback
272(9)
7.2.1 Solution Based on Dynamics Decomposition Forms
272(4)
7.2.2 Solution Based on Standard Decomposition
276(3)
7.2.3 Solution Based on Canonical Equivalent Form for Derivative Feedback
279(2)
7.3 Impulse Elimination by Output Feedback
281(3)
7.3.1 Problem Formulation
281(1)
7.3.2 The Solution
282(2)
7.4 I-Controllablizability and I-Observablizability
284(9)
7.4.1 Basic Criterion
285(4)
7.4.2 Criteria Based on Equivalent Forms
289(4)
7.5 Impulsive Elimination by P-D Feedback
293(9)
7.5.1 Method I
294(4)
7.5.2 Method II
298(4)
7.6 Notes and References
302(3)
8 Pole Assignment and Stabilization
305(32)
8.1 Pole Assignment by State Feedback
305(10)
8.1.1 Problems Formulation
305(2)
8.1.2 Pole Assignment under R-Controllability
307(3)
8.1.3 Pole Assignment under S-Controllability
310(5)
8.2 Pole Assignment by P-D Feedback
315(3)
8.2.1 Problem Formulation
315(1)
8.2.2 The Solution
315(3)
8.3 Stabilizability and Detectability
318(6)
8.3.1 Stabilizability
319(2)
8.3.2 Detectability
321(3)
8.4 Stabilizing Controller Design
324(9)
8.4.1 Design Based on Standard Decomposition
324(3)
8.4.2 Design Based on Controllability Canonical Forms
327(3)
8.4.3 Design Based on Lyapunov Theory
330(3)
8.5 Notes and References
333(4)
9 Eigenstructure Assignment
337(32)
9.1 The Problem
338(7)
9.1.1 The Problem
339(1)
9.1.2 Interpretations of Requirements
340(4)
9.1.3 Problem Decomposition
344(1)
9.2 The Parametric Solution
345(7)
9.2.1 Solution of Closed-Loop Eigenvectors
345(2)
9.2.2 Solution of the Gain Matrix K
347(3)
9.2.3 The Algorithm for Problem 9.1
350(2)
9.3 The Left Eigenvector Matrix
352(4)
9.3.1 Preliminaries
352(1)
9.3.2 The Parametric Expressions
353(3)
9.4 Response of the Closed-Loop System
356(5)
9.4.1 The Canonical Form for the Closed-Loop System
356(2)
9.4.2 The Closed-Loop Response
358(3)
9.5 An Example
361(4)
9.5.1 The General Solutions
362(1)
9.5.2 Special Solutions
363(2)
9.6 Notes and References
365(4)
10 Optimal Control
369(20)
10.1 Introduction
369(2)
10.2 Optimal Linear Quadratic State Regulation
371(8)
10.2.1 Problem Formulation
371(1)
10.2.2 The Conversion
372(3)
10.2.3 The Optimal Regulator
375(2)
10.2.4 An Illustrative Example
377(2)
10.3 Time-Optimal Control
379(6)
10.3.1 Problem Formulation
379(1)
10.3.2 Time-Optimal Control of the Slow and Fast Subsystems
380(2)
10.3.3 The Solution
382(3)
10.4 Notes and References
385(4)
11 Observer Design
389(40)
11.1 Introduction
389(3)
11.1.1 State Observers
390(1)
11.1.2 Function K x Observers
391(1)
11.2 Descriptor State Observers
392(4)
11.2.1 Existence Condition
392(2)
11.2.2 Design Methods
394(2)
11.3 Eigenstructure Assignment Design
396(6)
11.3.1 Eigenstructure Assignment Result
397(2)
11.3.2 The Algorithm and Example
399(3)
11.4 Observer Design with Disturbance Decoupling
402(7)
11.4.1 Problem Formulation
403(1)
11.4.2 Preliminaries
403(3)
11.4.3 Constraints for Disturbance Decoupling
406(1)
11.4.4 The Example
407(2)
11.5 Normal Reduced-Order State Observers
409(8)
11.5.1 Normal Rank E-Order State Observers
409(3)
11.5.2 Normal-State Observers of Order n - m
412(5)
11.6 Normal Function K x Observers
417(7)
11.6.1 Conditions for Normal Function K x Observers
417(2)
11.6.2 Parametric Design for Normal Function Observers
419(5)
11.7 Notes and References
424(5)
Part III Appendices
A Some Mathematical Results
429(22)
A.1 Delta Function δ (.)
429(3)
A.2 Laplace Transform
432(2)
A.3 Determinants and Inverses of Block Matrices
434(3)
A.4 Nilpotent Matrices
437(4)
A.5 Some Operations of Linear Subspaces
441(2)
A.6 Kernels and Images of Matrices
443(2)
A.7 Singular Value Decomposition
445(6)
B Rank-Constrained Matrix Matching and Least Square Problems
451(14)
B.1 The Problems
451(1)
B.2 Preliminaries
452(3)
B.3 Solution to Problem B.1
455(3)
B.4 Solution to Problem B.2
458(3)
B.5 An Illustrative Example
461(1)
B.6 Proof of Lemma B.4
462(3)
C Generalized Sylvester Matrix Equations
465(12)
C.1 Introduction
465(1)
C.2 Preliminaries
466(2)
C.3 Solution Based on Right Coprime Factorization
468(4)
C.4 Solution Based on SVD
472(1)
C.5 An Example
473(4)
References 477(14)
Index 491