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Tables of Contents for Linear Systems Theory
Chapter/Section Title
Page #
Page Count
Authors
vii
2
Preface
ix
4
Introduction
xiii
1 Mathematical Background
1
56
1.1 Introduction
1
1
1.2 Metric Spaces and Contraction Mapping Theory
1
17
1.2.1 Metric Spaces
2
7
1.2.2 Mappings in Metric Spaces
9
5
1.2.3 Contraction Mappings and Fixed Points
14
4
1.3 Some Properties of Vectors and Matrices
18
35
1.3.1 Norms of Vectors and Matrices
18
12
1.3.2 Special Matrix Forms
30
11
1.3.3 Matrix functions
41
12
Problems
53
4
2 Mathematics of Dynamic Processes
57
50
2.1 Solution of Ordinary Differential Equations
57
32
2.1.1 Existence and Uniqueness Theorems
57
8
2.1.2 Solution of Linear Differential Equations
65
10
2.1.3 Laplace Transform
75
14
2.2 Solution of Difference Equations
89
14
2.2.1 General Solutions
89
3
2.2.2 Solution of Linear Difference Equations
92
3
2.2.3 Z-transform
95
8
Problems
103
4
3 Characterization of Systems
107
90
3.1 The Concept of Dynamic Systems
107
5
3.2 Equilibrium and Linearization
112
7
3.3 Continuous Linear Systems
119
25
3.3.1 State-Space Approach
119
2
3.3.2 Transfer Functions
121
4
3.3.3 Equations in Input-Output Form
125
4
3.3.4 Combinations
129
11
3.3.5 Adjoint and Dual Systems
140
4
3.4 Discrete Systems
144
5
3.5 Applications
149
42
3.5.1 Dynamic Systems in Engineering
149
24
3.5.2 Dynamic Systems in Social Sciences
173
18
Problems
191
6
4 Stability Analysis
197
46
4.1 The Elements of the Lyapunov Stability Theory
198
21
4.1.1 Lyapunov Functions
199
6
4.1.2 The stability of time-variant linear systems
205
1
4.1.3 The Stability of Time-Invariant Linear Systems
206
13
4.2 BIBO Stability
219
5
4.3 Applications
224
14
4.3.1 Applications in Engineering
224
5
4.3.2 Applications in the Social Sciences
229
9
Problems
238
5
5 Controllability
243
50
5.1 Continuous Systems
243
25
5.1.1 General Conditions
244
12
5.1.2 Time-Invariant Systems
256
8
5.1.3 Output and Trajectory Controllability
264
4
5.2 Discrete Systems
268
6
5.3 Applications
274
13
5.3.1 Dynamic Systems in Engineering
274
7
5.3.2 Applications in the Social Sciences
281
6
Problems
287
6
6 Observability
293
34
6.1 Continuous Systems
294
9
6.1.1 General Conditions
294
5
6.1.2 Time-Invariant Systems
299
4
6.2 Discrete Systems
303
4
6.3 Duality
307
3
6.4 Applications
310
12
6.4.1 Dynamic Systems in Engineering
310
6
6.4.2 Applications in the Social Sciences
316
6
Problems
322
5
7 Canonical Forms
327
48
7.1 Diagonal and Jordan Forms
329
4
7.2 Controllability Canonical Forms
333
9
7.3 Observability Canonical Forms
342
4
7.4 Applications
346
23
7.4.1 Dynamic Systems in Engineering
346
14
7.4.2 Applications in the Social Sciences and Economics
360
9
Problems
369
6
8 Realization
375
50
8.1 Realizability of Weighting Patterns
376
20
8.1.1 Realizability Conditions
377
3
8.1.2 Minimal Realizations
380
7
8.1.3 Time-Invariant Realizations
387
9
8.2 Realizability of Transfer Functions
396
11
8.2.1 Realizability Conditions
397
7
8.2.2 Minimal Realizations
404
3
8.3 Applications
407
12
8.3.1 Dynamic Systems in Engineering
407
5
8.3.2 Applications in the Social Sciences and Economics
412
7
Problems
419
6
9 Estimation and Design
425
38
9.1 The Eigenvalue Placement Theorem
426
5
9.2 Observers
431
4
9.3 Reduced-Order Observers
435
2
9.4 The Eigenvalue Separation Theorem
437
4
9.5 Applications
441
16
9.5.1 Dynamic Systems in Engineering
441
9
9.5.2 Applications in the Social Sciences and Economics
450
7
Problems
457
6
10 Advanced Topics
463
36
10.1 Nonnegative Systems
463
6
10.2 The Kalman-Bucy Filter
469
3
10.3 Adaptive Control Systems
472
12
10.4 Neural Networks
484
15
References
499
4
Index
503