Linear systems theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2009
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XV, 263 S. Ill., graph. Darst. |
| ISBN: | 9780691140216 |
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| 100 | 1 | |a Hespanha, João P. |d 1968- |e Verfasser |0 (DE-588)131487019 |4 aut | |
| 245 | 1 | 0 | |a Linear systems theory |c João P. Hespanha |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2009 | |
| 300 | |a XV, 263 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804139929155928064 |
|---|---|
| adam_text | CONTENTS
Preamble
xiii
LINEAR SYSTEMS I
-
BASIC CONCEPTS
I SYSTEM REPRESENTATION
1
State-space linear systems
5
1.1
State-Space Linear Systems
5
1.2
Block Diagrams
7
1.3
Exercises
10
2
Linearization
11
2.1
State-Space Nonlinear Systems
11
2.2
Local Linearization around an Equilibrium Point
11
2.3
Local Linearization around a Trajectory
14
2.4
Feedback Linearization
15
2.5
Exercises
19
3
Causality, time
invariance,
and linearity
22
3.1
Basic Properties of LTV/LTI Systems
22
3.2
Characterization of All Outputs to a Given Input
24
3.3
Impulse Response
25
3.4
Laplace Transform (review)
27
3.5
Transfer Function
27
3.6
Discrete-Time Case
28
3.7
Additional Notes
29
3.8
Exercise
30
4
Impulse response and transfer function of state-
space systems
31
4.1
Impulse Response and Transfer Function for LTI Systems
31
4.2
Discrete-Time Case
32
4.3
Elementary Realization Theory
32
4.4
Equivalent State-Space Systems
36
4.5
LTI Systems in
MATLAB®
38
4.6
Exercises
39
5
Solutions to ltv systems
41
5.1
Solution to Homogeneous Linear Systems
41
5.2
Solution to Nonhomogeneous Linear Systems
43
viii CONTENTS
5.3
Discrete-Time Case
44
5.4
Exercises
45
6
Solutions to lti systems
46
6.1
Matrix Exponential
46
6.2
Properties of the Matrix Exponential
47
6.3
Computation of Matrix Exponentials Using Laplace Transforms
49
6.4
The Importance of the Characteristic Polynomial
50
6.5
Discrete-Time Case
50
6.6
Symbolic Computations in
MATLAB®
51
6.7
Exercises
53
V Solutions to lti systems: the
jordan
ndrmal form 55
7.1
Jordan Normal Form
55
7.2
Computation of Matrix Powers Using the Jordan Normal Form
5 7
7.3
Computation of Matrix Exponentials Using the Jordan Normal Form
58
7.4
Eigenvalues with Multiplicity Larger than
1 59
7.5
Exercise
60
1
1 STABILITY
61
8
Internal dr lyapunov stability
63
8.1
Matrix Norms (review)
63
8.2
Lyapunov Stability
65
8.3
Eigenvalue Conditions for Lyapunov Stability
66
8.4
Positive-Definite Matrices (review)
67
8.5
Lyapunov Stability Theorem
67
8.6
Discrete-Time Case
70
8.7
Stability of Locally Linearized Systems
72
8.8
Stability Tests with
MATLAB®
77
8.9
Exercises
78
9
Input-output stability
80
9.1
Bounded-Input, Bounded-Output Stability
80
9.2
Time Domain Conditions for
BIBO
Stability
81
9.3
Frequency Domain Conditions for
BIBO
Stability
84
9.4
BIBO
versus Lyapunov Stability
85
9.5
Discrete-Time Case
85
9.6
Exercises
86
1
D
Preview of optimal control
87
10.1
The Linear Quadratic Regulator Problem
87
10.2
Feedback Invariants
88
10.3
Feedback Invariants in Optimal Control
88
10.4
Optimal State Feedback
89
10.5
LQR with
MATLAB®
91
CONTENTS «
10.6
Exercises
91
IM CDNTRDLLABILITY
AND STATE FEEDBACK
93
1 1
CDNTRDLLABLE AND REACHABLE
SUBSPACES 95
11.1
Controllable and Reachable Subspaces
95
11.2
Physical Examples and System Interconnections
96
11.3
Fundamental Theorem of Linear Equations (review)
99
11.4
Reachability and Controllability Gramians
100
11.5
Open-Loop Minimum-Energy Control
101
11.6
Controllability Matrix (LTI)
102
11.7
Discrete-Time Case
105
11.8
MATLAB®
Commands
109
11.9
Exercise
109
1 2
Controllable systems
110
12.1
Controllable Systems
110
12.2
Eigenvector Test for Controllability 111
12.3
Lyapunov Test for Controllability
113
12.4
Feedback Stabilization Based on the Lyapunov Test
116
12.5
Exercises
117
1 3
Controllable decompositions
118
13.1
Invariance
with Respect to Similarity Transformations
118
13.2
Controllable Decomposition
119
13.3
Block Diagram Interpretation
120
13.4
Transfer Function
121
13.5
MATLAB®
Commands
122
13.6
Exercise
122
1 4
Stabilizability
123
14.1
Stabilizable System
123
14.2
Eigenvector Test for Stabilizability
124
14.3
Popov-Belevitch-Hautus (PBH) Test for Stabilizability
125
14.4
Lyapunov Test for Stabilizability
126
14.5
Feedback Stabilization Based on the Lyapunov Test
127
14.6
Eigenvalue Assignment
128
14.7
MATLAB®
Commands
129
14.8
Exercises
129
IV OBSERVABILITY AND OUTPUT FEEDBACK
133
1 5
Dbservability
135
15.1
Motivation: Output Feedback
135
CONTENTS
15.2 Unobservable Subspace 136
15.3 Unconstructible Subspace 137
15.4
Physical Examples
138
15.5
Observability and Constructibility
Gramians 139
15.6
Gramian-based Reconstruction
140
15.7
Discrete-Time Case
141
15.8
Duality
(Ш)
142
15.9
Observability Tests
144
15.10MATLAB® Commands
145
15.11
Exercises
145
1 6
Output feedback
148
16.1
Observable Decomposition
148
16.2
Kalman
Decomposition Theorem
149
16.3
Detectability
152
16.4
Detectability Tests
152
16.5
State Estimation
153
16.6
Eigenvalue Assignment by Output Injection
154
16.7
Stabilization through Output Feedback
155
16.8
MATLAB®
Commands
156
16.9
Exercises
156
1 7
Minimal realizations
157
17.1
Minimal Realizations
157
17.2
Markov Parameters
158
17.3
Similarity of Minimal Realizations
160
17.4
Order of a Minimal
SISO
Realization
161
17.5
MATLAB®
Commands
163
17.6
Exercises
163
LINEAR SYSTEMS II-ADVANCED MATERIAL
V POLES AND ZEROS OF
MIMO
SYSTEMS
167
1
S
Smith-McMillan form
169
18.1
Informal Definition of Poles and Zeros
169
18.2
Polynomial Matrices: Smith Form
170
18.3
Rational Matrices: Smith-McMillan Form
172
18.4
McMillan Degree, Poles, and Zeros
173
18.5
Transmission-Blocking Property of Transmission Zeros
175
18.6
MATLAB®
Commands
176
18.7
Exercises
176
CONTENTS xi
1 9
State-space zerds, minimality, and system inverses
177
19.1
Poles of Transfer Functions versus Eigenvalues of State-Space Real¬
izations
177
19.2
Transmission Zeros of Transfer Functions versus Invariant Zeros of
State-Space Realizations
178
19.3
Order of Minimal Realizations
180
19.4
System Inverse
182
19.5
Existence of an Inverse
183
19.6
Poles and Zeros of an Inverse
184
19.7
Feedback Control of Stable Systems with Stable Inverses
185
19.8
MATLAB®
Commands
186
19.9
Exercises
187
VI LQR/LgG DPTIMAL CDNTRDL
189
2O Linear quadratic
régulation
(LulR)
191
20.1
Deterministic Linear Quadratic Regulation (LQR)
191
20.2
Optimal Regulation
192
20.3
Feedback Invariants
193
20.4
Feedback Invariants in Optimal Control
193
20.5
Optimal State Feedback
194
20.6
LQR in
MATLAB®
195
20.7
Additional Notes
196
20.8
Exercises
196
2 1
The algebraic riccati equation (ARE)
197
21.1
The Hamiltonian Matrix
197
21.2
Domain of the Riccati Operator
198
21.3
Stable Subspaces
199
21.4
Stable Subspace of the Hamiltonian Matrix
199
21.5
Exercises
203
2 2
Frequency domain and asymptotic properties
df LQR
204
22.1
Kalman s Equality
204
22.2
Frequency Domain Properties: Single-Input Case
205
22.3
Loop Shaping using LQR: Single-Input Case
207
22.4
LQR Design Example
210
22.5
Cheap Control Case
213
22.6
MATLAB®
Commands
216
22.7
Additional Notes
216
22.8
The Loop-shaping Design Method (review)
217
22.9
Exercises
222
2 3
DUTPUT FEEDBACK
223
23.1
Certainty Equivalence
223
xii CONTENTS
23.2
Deterministic Minimum-Energy Estimation
(MEE)
223
23.3
Stochastic Linear Quadratic Gaussian (LQG) Estimation
228
23.4
LQR/LQG Output Feedback
229
23.5
Loop Transfer Recovery (LTR)
230
23.6
Optimal Set Point Control
231
23.7
LQR/LQG with
MATLAB®
235
23.8
LTR Design Example
235
23.9
Exercises
236
24
LQG/LQR AND THE
Q
PARAMETERIZATION
238
24.1
Q
-augmented LQG/LQR Controller
238
24.2
Properties
239
24.3
Q
Parameterization
241
24.4
Exercise
242
25
Q
DESIGN
243
25.1
Control Specifications for
Q
Design
243
25.2
The
Q
Design Feasibility Problem
246
25.3
Finite-dimensional Optimization:
Ritz
Approximation
246
25.4
Q
Design using
MATLAB®
and CVX
248
25.5
β
Design Example
253
25.6
Exercise
255
Bibliography
257
index
259
Linear
systems theory is the cornerstone of control
theory and a well-established discipline that focuses
on linear differential equations from the perspective of
control and estimation. In this textbook,
João
Hcspanha
covers the key topics of the field in a unique lecture-
style format, making the book easy to use for instructors
and students. He looks at system representation, stabil¬
ity, controllability and state feedback, observability and
state estimation, and realization theory. He provides
the
backiïround
for advanced modern control desien
techniques and feedback linearization, and examines
advanced Ibundational topics such as
multivariable
poles
and zeros, and LQG/LQR.
The textbook presents only the most essential math¬
ematical derivations, and places comments, discussion,
and terminology in sidebars so that readers can follow
the core material easily and without distraction. An¬
notated proofs with sidebars explain the techniques of
proof construction, including contradiction, contraposi¬
tion, cycles of implications to prove equivalence, and the
difference between necessity and sufficiency. Annotated
theoretical developments also use sidebars to discuss
relevant commands available in
MATLAB©,
allowing
students to understand these important tools.
The balanced chapters can each be covered in ap¬
proximately two hours of lecture time, simplifying
course planning and student review. Solutions to
the theoretical and computational exercises are also
available for instructors.
Easy-to-use textbook in unique lecture-style
format
Sidebars explain topics in further detail
Annotated proofs and discussions of
MATLAB
commands
Balanced chapters can each be taught in two
hours of course lecture
Solutions to exercises available to instructors
|
| any_adam_object | 1 |
| author | Hespanha, João P. 1968- |
| author_GND | (DE-588)131487019 |
| author_facet | Hespanha, João P. 1968- |
| author_role | aut |
| author_sort | Hespanha, João P. 1968- |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| callnumber-raw | QA402 |
| callnumber-search | QA402 |
| callnumber-sort | QA 3402 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 880 SK 960 |
| classification_tum | MSR 655f MSR 580f |
| ctrlnum | (OCoLC)305421771 (DE-599)BVBBV035719013 |
| dewey-full | 003/.74 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 003 - Systems |
| dewey-raw | 003/.74 |
| dewey-search | 003/.74 |
| dewey-sort | 13 274 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik Mathematik Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik |
| format | Book |
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| id | DE-604.BV035719013 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:51:53Z |
| institution | BVB |
| isbn | 9780691140216 |
| language | English |
| lccn | 2009006371 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017995832 |
| oclc_num | 305421771 |
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| owner_facet | DE-20 DE-19 DE-BY-UBM DE-706 DE-91G DE-BY-TUM DE-11 DE-824 DE-739 |
| physical | XV, 263 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| spelling | Hespanha, João P. 1968- Verfasser (DE-588)131487019 aut Linear systems theory João P. Hespanha Princeton [u.a.] Princeton Univ. Press 2009 XV, 263 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Linear systems Textbooks System analysis Textbooks Kontrolltheorie (DE-588)4032317-1 gnd rswk-swf Systemtheorie (DE-588)4058812-9 gnd rswk-swf Systemtheorie (DE-588)4058812-9 s Kontrolltheorie (DE-588)4032317-1 s DE-604 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017995832&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017995832&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Hespanha, João P. 1968- Linear systems theory Linear systems Textbooks System analysis Textbooks Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| subject_GND | (DE-588)4032317-1 (DE-588)4058812-9 |
| title | Linear systems theory |
| title_auth | Linear systems theory |
| title_exact_search | Linear systems theory |
| title_full | Linear systems theory João P. Hespanha |
| title_fullStr | Linear systems theory João P. Hespanha |
| title_full_unstemmed | Linear systems theory João P. Hespanha |
| title_short | Linear systems theory |
| title_sort | linear systems theory |
| topic | Linear systems Textbooks System analysis Textbooks Kontrolltheorie (DE-588)4032317-1 gnd Systemtheorie (DE-588)4058812-9 gnd |
| topic_facet | Linear systems Textbooks System analysis Textbooks Kontrolltheorie Systemtheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017995832&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017995832&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hespanhajoaop linearsystemstheory |