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E-raamat: Linear Continuous-Time Systems

(University of Technology of BelfortMontbéliard, France (Retired))
  • Formaat: 495 pages
  • Ilmumisaeg: 28-Jul-2017
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351642897
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Linear Continuous-Time SystemsSuurem pilt
  • Formaat: 495 pages
  • Ilmumisaeg: 28-Jul-2017
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9781351642897
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This book aims to help the reader understand the linear continuous-time time-invariant dynamical systems theory and its importance for systems analysis and design of the systems operating in real conditions, i.e., in forced regimes under arbitrary initial conditions. The text completely covers IO, ISO and IIO systems. It introduces the concept of the system full matrix P(s) in the complex domain and establishes its link with the also newly introduced system full transfer function matrix F(s). The text establishes the full block diagram technique based on the use of F(s), which incorporates the Laplace transform of the input vector and the vector of all initial conditions. It explores the direct relationship between the system full transfer function matrix F(s) and the Lyapunov stability concept, definitions and conditions, as well as with the BI stability concept, definitions, and conditions. The goal of the book is to unify the study and applications of all three classes of the of the linear continuous-time time-invariant systems, for short systems.
List of Figures
xiii
Preface xvii
I BASIC TOPICS OF LINEAR CONTINUOUS-TIME TIME-INVARIANT DYNAMICAL SYSTEMS
1(90)
1 Introduction
3(18)
1.1 Time
3(3)
1.2 Time, physical principles, and systems
6(2)
1.3 Time and system dynamics
8(3)
1.4 Systems and complex domain
11(7)
1.5 Notational preliminaries
18(3)
2 Classes of systems
21(16)
2.1 IO systems
21(8)
2.2 ISO systems
29(2)
2.3 IIO systems
31(6)
3 System Regimes
37(52)
3.1 System regime meaning
37(1)
3.2 System regimes and initial conditions
38(1)
3.3 Forced and free regimes
39(8)
3.3.1 Introduction
39(1)
3.3.2 The temporal domain descriptions. The independent variable is time t ε
40(1)
3.3.3 The complex domain system descriptions. The independent variable is the complex variable s ε C
41(5)
3.3.4 Basic problem
46(1)
3.4 Desired regime
47(13)
3.4.1 Introduction
47(2)
3.4.2 IO systems
49(3)
3.4.3 ISO systems
52(4)
3.4.4 IIO systems
56(4)
3.5 Deviations and mathematical models
60(7)
3.5.1 Introduction
60(2)
3.5.2 IO systems
62(1)
3.5.3 ISO systems
63(1)
3.5.4 IIO systems
64(3)
3.6 Stationary and nonstationary regimes
67(11)
3.6.1 Introduction
67(1)
3.6.2 IO systems
68(4)
3.6.3 ISO systems
72(3)
3.6.4 IIO systems
75(3)
3.7 Equilibrium regime
78(11)
3.7.1 Introduction
78(1)
3.7.2 IO systems
79(2)
3.7.3 ISO systems
81(3)
3.7.4 IIO systems
84(5)
4 Transfer function matrix G(s)
89(2)
II FULL TRANSFER FUNCTION MATRIX F(S) AND SYSTEM REALIZATION
91(146)
5 Problem statement
93(2)
6 Nondegenerate matrices
95(8)
7 Definition of F(s)
103(18)
7.1 Definition of F(s) in general
103(2)
7.2 Definition of F(s) of the IO system
105(5)
7.3 Definition of F(s) of the ISO system
110(4)
7.4 Definition of F(s) of the IIO system
114(7)
8 Determination of F(s)
121(34)
8.1 F(s) of the IO system
121(12)
8.2 F(s) of the ISO system
133(14)
8.3 F(s) of the IIO system
147(6)
8.4 Conclusion: Common general form of F(s)
153(2)
9 Full block diagram algebra
155(16)
9.1 Introduction
155(2)
9.2 Parallel connection
157(3)
9.3 Connection in series
160(4)
9.4 Feedback connection
164(7)
10 Physical meaning of F(s)
171(14)
10.1 The IO system
171(4)
10.2 The ISO system
175(4)
10.3 The IIO system
179(6)
11 System matrix and equivalence
185(20)
11.1 System matrix of the IO system
185(7)
11.2 System matrix of the ISO System
192(8)
11.3 System matrix of the IIO system
200(5)
12 Realizations of F(s)
205(32)
12.1 Dynamical and least dimension of a system
205(3)
12.2 On realization and minimal realization
208(2)
12.2.1 Minimal realization of the transfer function matrix
208(1)
12.2.2 Realization and minimal realization of the full transfer function matrix and the system
209(1)
12.3 Realizations of F(s) of IO systems
210(9)
12.4 Realizations of F(s) of ISO systems
219(14)
12.5 Realizations of F(s) of IIO systems
233(4)
III STABILITY STUDY
237(120)
13 Lyapunov stability
239(78)
13.1 Lyapunov stability concept
239(3)
13.2 Lyapunov stability definitions
242(33)
13.2.1 IO systems
242(11)
13.2.2 ISO systems
253(8)
13.2.3 IIO systems
261(14)
13.3 Lyapunov method and theorems
275(16)
13.3.1 Outline of Lyapunov's original theory
275(2)
13.3.2 Lyapunov method, theorems and methodology for the linear systems
277(9)
13.3.3 Lyapunov theorem for the IO systems
286(2)
13.3.4 Lyapunov theorem for the ISO systems
288(1)
13.3.5 Lyapunov theorem for the IIO systems
289(2)
13.4 Lyapunov stability conditions via F(s)
291(26)
13.4.1 Generating theorem
291(6)
13.4.2 IO systems
297(7)
13.4.3 ISO systems
304(5)
13.4.4 IIO systems
309(8)
14 Bounded Input stability
317(40)
14.1 BI stability and initial conditions
317(3)
14.2 BI stability definitions
320(10)
14.2.1 IO systems
320(2)
14.2.2 ISO systems
322(4)
14.2.3 IIO systems
326(4)
14.3 BI stability conditions
330(27)
14.3.1 IO systems
330(10)
14.3.2 ISO systems
340(5)
14.3.3 IIO systems
345(12)
IV CONCLUSION
357(10)
15 Motivation for the book
359(4)
16 Summary of the contributions
363(2)
17 Future teaching and research
365(2)
V BIBLIOGRAPHY
367(14)
VI APPENDICES
381(74)
A Notation
383(16)
A.1 Abbreviations
383(1)
A.2 Indexes
384(1)
A.2.1 Subscripts
384(1)
A.2.2 Superscript
384(1)
A.3 Letters
384(1)
A.3.1 Blackboard bold letters
384(1)
A.3.2 Calligraphic letters
385(1)
A.3.3 Fraktur letters
385(2)
A.3.4 Greek letters
387(1)
A.3.5 Roman letters
388(6)
A.4 Names
394(1)
A.5 Symbols and vectors
395(2)
A.6 Units
397(2)
B Laplace transforms and Dirac impulses
399(18)
B.1 Laplace transforms
399(2)
B.2 Dirac impulses
401(16)
C System forms
417(8)
C.1 From IO system to ISO system
417(4)
C.2 From ISO system to IO system
421(1)
C.3 Relationships among system descriptions
422(3)
D Proof of Theorem 142
425(4)
E Example: F(s) of a MIMO system
429(6)
F Proof of Theorem 165
435(6)
G Proof for Example 167
441(6)
H Proof of Theorem 168
447(2)
I Proof of Theorem 176
449(2)
J Proof of Theorem 179
451(2)
K Proof of Theorem 183
453(2)
VII INDEX
455
Lyubomir T. Gruyitch is Certified Mechanical Engineer (Dipl. M. Eng.), Master of Electrical Engineering Sciences (M. E. E. Sc.), and Doctor of Engineering Sciences (D. Sc.) (all with the University of Belgrade -UB, Serbia). Dr. Gruyitch was a leading contributor to the creation of the research Laboratory of Automatic Control, Mechatronics, Manufacturing Engineering and Systems Engineering of the National School of Engineers (Belfort, France), and a founder of the educational division and research Laboratory of Automatic Control of the Faculty of Mechanical Engineering, UB . He has given invited university seminars in Belgium, Canada, England, France, Russia, Serbia, Tunis, and USA. He has published 8 books (7 in English, 1 in Serb), 4 textbooks (in Serbo-Croatian), 11 lecture notes (7 in French, 2 in English, 2 in Serbo-Croatian), one manual of solved problems, one book translation from Russian, chapters in eight scientific books, 130 scientific papers in scientific journals, 173 conference research papers, and 2 educational papers. France honored him Doctor Honoris Causa (DHC).
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