Linear control theory: structure, robustness, and optimization
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla.
CRC
2009
London Taylor & Francis |
| Series: | Automation and control engineering
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 911 S. Ill., graph. Darst. 26cm |
| ISBN: | 0849340632 9780849340635 |
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| 020 | |a 0849340632 |c (hbk.) : £84.00 |9 0-8493-4063-2 | ||
| 020 | |a 9780849340635 |9 978-0-8493-4063-5 | ||
| 035 | |a (OCoLC)144565585 | ||
| 035 | |a (DE-599)HBZHT015796895 | ||
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| 100 | 1 | |a Bhattacharyya, Shankar P. |d 1946- |e Verfasser |0 (DE-588)121269442 |4 aut | |
| 245 | 1 | 0 | |a Linear control theory |b structure, robustness, and optimization |c Shankar P. Bhattacharyya ; Aniruddha Datta ; L. H. Keel |
| 264 | 1 | |a Boca Raton, Fla. |b CRC |c 2009 | |
| 264 | 1 | |a London |b Taylor & Francis | |
| 300 | |a XVIII, 911 S. |b Ill., graph. Darst. |c 26cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Automation and control engineering |v 33 | |
| 650 | 4 | |a Regelungstheorie | |
| 650 | 4 | |a Linear control systems | |
| 650 | 4 | |a Control theory | |
| 650 | 0 | 7 | |a Lineare Regelung |0 (DE-588)4035819-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Regelung |0 (DE-588)4035819-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Datta, Aniruddha |d 1963- |e Verfasser |0 (DE-588)118107526 |4 aut | |
| 700 | 1 | |a Keel, Lee H. |e Verfasser |4 aut | |
| 830 | 0 | |a Automation and control engineering |v 33 |w (DE-604)BV021743861 |9 33 | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017144037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017144037 | ||
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| _version_ | 1804138655477923840 |
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| adam_text | Contents
PREFACE
xvii
I THREE TERM CONTROLLERS
1
1 PID
CONTROLLERS:
AN OVERVIEW OF CLASSICAL THEORY
3
1.1
Introduction to Control
..................... 3
1.2
The Magic of Integral Control
.................. 5
1.3 PID
Controllers
.......................... 8
1.4
Classical
PID
Controller Design
................. 10
1.4.1
The Ziegler-Nichols Step Response Method
...... 10
1.4.2
The Ziegler-Nichols Frequency Response Method
... 11
1.4.3 PID
Settings Using the Internal Model Controller
Design Technique
..................... 15
1.4.4
Dominant Pole Design: The Cohen-Coon Method
... 17
1.4.5
New Tuning Approaches
................. 17
1.5
Integrator Windup
........................ 19
1.5.1
Setpoint Limitation
.................... 20
1.5.2
Back-Calculation and Tracking
............. 20
1.5.3
Conditional Integration
................. 21
1.6
Exercises
.............................. 21
1.7
Notes and References
....................... 24
2 PID
CONTROLLERS FOR DELAY-FREE LTI SYSTEMS
25
2.1
Introduction
........................... 25
2.2
Stabilizing Set
........................... 27
2.3
Signature Formulas
........................ 29
2.3.1
Computation of
σ(ρ)
............ ....... 30
2.3.2
Alternative Signature Expression
............ 32
2.4
Computation of the
PID
Stabilizing Set
............ 33
2.5 PID
Design with Performance Requirements
.......... 38
2.5.1
Signature Formulas for Complex Polynomials
..... 40
2.5.2
Complex
PID
Stabilization Algorithm
......... 42
2.5.3 PID
Design with Guaranteed Gain and Phase Margins
44
2.5.4
Synthesis of
PID
Controllers with an H^ Criterion
. . 44
2.5.5 PID
Controller Design for Hoo Robust Performance
. 49
Linear
Control
Theory
2.6
Exercises
.............................. 52
2.7
Notes and References
....................... 54
PID
CONTROLLERS FOR SYSTEMS
WITH TIME DELAY
55
3.1
Introduction
............................ 55
3.2
Characteristic Equations for Delay Systems
.......... 57
3.3
The
Padé
Approximation and Its Limitations
......... 60
3.3.1
First Order
Padé
Approximation
............ 62
3.3.2
Higher Order
Padé
Approximations
........... 65
3.4
The Hermite-Biehler Theorem for Quasi-polynomials
..... 69
3.4.1
Applications to Control Theory
............. 71
3.5
Stability of Systems with a Single Delay
............ 77
3.6 PID
Stabilization of First Order Systems with Time Delay
. . 85
3.6.1
The
PID
Stabilization Problem
............. 86
3.6.2
Open-Loop Stable Plant
................. 87
3.6.3
Open-Loop Unstable Plant
............... 105
3.7 PID
Stabilization of Arbitrary LTI Systems with
a Single Time Delay
....................... 116
3.7.1
Connection between Pontryagin s Theory and
the Nyquist Criterion
.................. 117
3.7.2
Problem Formulation and Solution Approach
..... 121
3.7.3
Proportional Controllers
................. 123
3.7.4
PI Controllers
....................... 126
3.7.5 PID
Controllers for an Arbitrary LTI Plant with Delay
128
3.8
Proofs of Lemmas
3.3, 3.4,
and
3.5 ............... 135
3.8.1
Preliminary Results
................... 135
3.8.2
Proof of Lemma
3.3 ................... 139
3.8.3
Proof of Lemma
3.4................... 141
3.8.4
Proof of Lemma
3.5 ................... 141
3.9
Proofs of Lemmas
3.7
and
3.9.................. 144
3.9.1
Proof of Lemma
3.7................... 144
3.9.2
Proof of Lemma
3.9 ................... 145
3.10
An Example of Computing the Stabilizing Set
......... 148
3.11
Exercises
.............................. 150
3.12
Notes and References
....................... 151
DIGITAL
PID
CONTROLLER DESIGN
153
4.1
Introduction
............................153
4.2
Preliminaries
...........................155
4.3
Tchebyshev Representation and Root Clustering
.......156
4.3.1
Tchebyshev Representation of Real Polynomials
.... 156
4.3.2
Interlacing Conditions for Root Clustering and
Schur
Stability
..........................158
4.3.3
Tchebyshev Representation of Rational Functions
. . . 159
Table
of Contents
xi
4.4
Root Counting Formulas
.....................160
4.4.1
Phase Unwrapping and Root Distribution
.......160
4.4.2
Root Counting and Tchebyshev Representation
.... 161
4.5
Digital PI, PD, and
PID
Controllers
..............163
4.6
Computation of the Stabilizing Set
...............165
4.6.1
Constant Gain Stabilization
...............165
4.6.2
Stabilization with PI Controllers
............168
4.6.3
Stabilization with PD Controllers
............169
4.7
Stabilization with
PID
Controllers
...............170
4.7.1
Maximally Deadbeat Control
........:.....173
4.7.2
Maximal Delay Tolerance Design
............175
4.8
Exercises
..............................179
4.9
Notes and References
.......................179
5
FIRST ORDER CONTROLLERS FOR LTI SYSTEMS
181
5.1
Root Invariant Regions
...................... 181
5.2
An Example
............................ 185
5.3
Robust Stabilization by First Order Controllers
........ 189
5.4
Hoc Design with First Order Controllers
............ 190
5.5
First Order Discrete-Time Controllers
............. 195
5.5.1
Computation of Root Distribution Invariant Regions
. 196
5.5.2
Delay Tolerance
...................... 201
5.6
Exercises
.............................. 205
5.7
Notes and References
....................... 206
6
CONTROLLER SYNTHESIS FREE OF
ANALYTICAL MODELS
207
6.1
Introduction
............................208
6.2
Mathematical Preliminaries
...................210
6.3
Phase, Signature, Poles, Zeros, and Bode Plots
........215
6.4 PID
Synthesis for Delay Free Continuous-Time Systems
. . . 218
6.5 PID
Synthesis for Systems with Delay
.............222
6.6 PID
Synthesis for Performance
.................224
6.7
An Illustrative Example:
PID
Synthesis
............227
6.8
Model Free Synthesis for First Order Controllers
.......232
6.9
Model Free Synthesis of First Order Controllers for
Performance
............................237
6.10
Data Based Design vs. Model Based Design
..........240
6.11
Data-Robust Design via Interval Linear Programming
.... 243
6.11.1
Data Robust
PID
Design
................244
6.12
Computer-Aided Design
.....................251
6.13
Exercises
..............................255
6.14
Notes and References
.......................257
xii
Linear
Control
Theory
7
DATA DRIVEN SYNTHESIS OF THREE
TERM DIGITAL CONTROLLERS
259
7.1
Introduction
............................259
7.2
Notation and Preliminaries
...................260
7.3 PID
Controllers for Discrete-Time Systems
..........262
7.4
Data Based Design: Impulse Response Data
..........270
7.4.1
Example: Stabilizing Set from Impulse Response
. . . 273
7.4.2
Sets Satisfying Performance Requirements
.......276
7.5
First Order Controllers for Discrete-Time Systems
......278
7.6
Computer-Aided Design
.....................282
7.7
Exercises
..............................288
7.8
Notes and References
.......................289
II ROBUST PARAMETRIC CONTROL
291
8
STABILITY THEORY FOR POLYNOMIALS
293
8.1
Introduction
............................293
8.2
The Boundary Crossing Theorem
................294
8.2.1
Zero Exclusion Principle
.................301
8.3
The Hermite-Biehler Theorem
..................302
8.3.1
Hurwitz Stability
.....................302
8.3.2
Hurwitz Stability for Complex Polynomials
......310
8.3.3 Schur
Stability
......................312
8.3.4
General Stability Regions
................319
8.4 Schur
Stability Test
.......................319
8.5
Hurwitz Stability Test
......................322
8.5.1
Root Counting and the Routh Table
..........326
8.5.2
Complex Polynomials
..................327
8.6
Exercises
..............................328
8.7
Notes and References
.......................332
9
STABILITY OF A LINE SEGMENT
333
9.1
Introduction
............................333
9.2
Bounded Phase Conditions
...................334
9.3
Segment Lemma
.........................341
9.3.1
Hurwitz Case
.......................341
9.4 Schur
Segment Lemma via Tchebyshev Representation
.... 345
9.5
Some Fundamental Phase Relations
..............348
9.5.1
Phase Properties of Hurwitz Polynomials
.......348
9.5.2
Phase Relations for a Segment
.............356
9.6
Convex Directions
........................359
9.7
The Vertex Lemma
........................369
9.8
Exercises
..............................374
9.9
Notes and References
.......................378
Table
of Contents
xiii
10
STABILITY MARGIN COMPUTATION
379
10.1
Introduction
............................ 379
10.2
The Parametric Stability Margin
................ 380
10.2.1
The Stability Ball in Parameter Space
......... 380
10.2.2
The Image Set Approach
................ 382
10.3
Stability Margin Computation
.................. 384
10.3.1
£2 Stability Margin
.................... 387
10.3.2
Discontinuity of the Stability Margin
.......... 391
10.3.3
e2 Stability Margin for Time-Delay Systems
...... 392
10.3.4
£oo and
ίλ
Stability Margins
............... 395
10.4
The Mapping Theorem
...................... 396
10.4.1
Robust Stability via the Mapping Theorem
...... 399
10.4.2
Refinement of the Convex Hull Approximation
.... 402
10.5
Stability Margins of Multilinear Interval Systems
....... 405
10.5.1
Examples
......................... 407
10.6
Robust Stability of Interval Matrices
.............. 416
10.6.1
Unity Rank Perturbation Structure
........... 416
10.6.2
Interval Matrix Stability via the Mapping Theorem
. . 417
10.6.3
Numerical Examples
.................... 418
10.7
Robustness Using a Lyapunov Approach
............ 423
10.7.1
Robustification Procedure
................ 427
10.8
Exercises
.............................. 432
10.9
Notes and References
....................... 441
11
STABILITY OF A POLYTOPE
443
11.1
Introduction
............................ 443
11.2
Stability of Polytopic Families
.................. 444
11.2.1
Exposed Edges and Vertices
............... 445
11.2.2
Bounded Phase Conditions for Checking Robust
Stability of Polytopes
.................. 448
11.2.3
Extremal Properties of Edges and Vertices
....... 452
11.3
The Edge Theorem
........................ 455
11.3.1
Edge Theorem
...................... 456
11.3.2
Examples
......................... 464
11.4
Stability of Interval Polynomials
................ 470
11.4.1
Kharitonov s Theorem for Real Polynomials
...... 470
11.4.2
Kharitonov s Theorem for Complex Polynomials
. . . 478
11.4.3
Interlacing and Image Set
................ 481
11.4.4
Image Set Based Proof of Kharitonov s Theorem
. . . 484
11.4.5
Image Set Edge Generators and Exposed Edges
.... 485
11.4.6
Extremal Properties of the Kharitonov Polynomials
.487
11.4.7
Robust State Feedback Stabilization
.......... 492
11.5
Stability of Interval Systems
................... 498
11.5.1
Problem Formulation and Notation
...........500
11.5.2
The Generalized Kharitonov Theorem
......... 504
xiv
Linear Control Theory
11.5.3
Comparison with the Edge Theorem
..........514
11.5.4
Examples
.........................515
11.5.5
Image Set Interpretation
.................521
11.6
Polynomic Interval Families
...................522
11.6.1
Robust
Positivity
.....................524
11.6.2
Robust Stability
......................528
11.6.3
Application to Controller Synthesis
...........532
11.7
Exercises
..............................536
11.8
Notes and References
.......................546
12
ROBUST CONTROL DESIGN
549
12.1
Introduction
............................549
12.2
Interval Control Systems
.....................551
12.3
Frequency Domain Properties
..................553
12.4
Nyquist, Bode, and Nichols Envelopes
.............563
12.5
Extremal Stability Margins
...................573
12.5.1
Guaranteed Gain and Phase Margins
..........574
12.5.2
Worst Case Parametric Stability Margin
........574
12.6
Robust Parametric Classical Design
...............577
12.6.1
Guaranteed Classical Design
...............577
12.6.2
Optimal Controller Parameter Selection
........588
12.7
Robustness Under Mixed Perturbations
............591
12.7.1
Small Gain Theorem
...................592
12.7.2
Small Gain Theorem for Interval Systems
.......593
12.8
Robust Small Gain Theorem
..................602
12.9
Robust Performance
.......................606
12.10
The Absolute Stability Problem
.................609
12.11
Characterization of the SPR Property
.............615
12.11.1
SPR Conditions for Interval Systems
..........617
12.12
The Robust Absolute Stability Problem
............625
12.13
Exercises
..............................632
12.14
Notes and References
.......................637
III OPTIMAL AND ROBUST CONTROL
639
13
THE LINEAR QUADRATIC REGULATOR
641
13.1
An Optimal Control Problem
..................641
13.1.1
Principle of Optimality
·..................642
13.1.2
Hamilton-
J
acobi-Bellman Equation
...........642
13.2
The Finite-Time LQR Problem
.................645
13.2.1
Solution of the Matrix
Ricatti
Differential Equation
. 647
13.2.2
Cross Product Terms
...................647
13.3
The Infinite Horizon LQR Problem
...............648
13.3.1
General Conditions for Optimality
...........648
13.3.2
The Infinite Horizon LQR Problem
...........650
Table
of Contents
xv
13.4
Solution of the Algebraic Riccati Equation
........... 651
13.5
The LQR as an Output Zeroing Problem
............ 658
13.6
Return Difference Relations
................... 660
13.7
Guaranteed Stability Margins for the LQR
........... 661
13.7.1
Gain Margin
.......................663
13.7.2
Phase Margin
.......................663
13.7.3
Single Input Case
.....................664
13.8
Eigenvalues of the Optimal Closed Loop System
........665
13.8.1
Closed-Loop Spectrum
..................665
13.9
Optimal Dynamic Compensators
................667
13.9.1
Dual Compensators
...................670
13.10
Servomechanisms and Regulators
................672
13.10.1
Notation and Problem Formulation
...........672
13.10.2
Reference and Disturbance Signal Classes
.......673
13.10.3
Solution of the Servomechanism Problem
.......673
13.11
Exercises
..............................680
13.12
Notes and References
.......................687
14
SISO
Яоо
AND
h
OPTIMAL CONTROL
689
14.1
Introduction
............................689
14.2
The Small Gain Theorem
....................693
14.3
^-Stability and Robustness via the Small Gain Theorem
. . . 704
14.4
YJBK Parametrization of All Stabilizing
Compensators (Scalar Case)
...................709
14.5
Control Problems in the
Я^
Framework
............716
14.6
Яоо
Optimal Control:
SISO
Case
................725
14.6.1
Dual Spaces
........................729
14.6.2
Inner Product Spaces
..................733
14.6.3
Orthogonality and Alignment in
Noninner
Product Spaces
......................736
14.6.4
The All-Pass Property of H^ Optimal Controllers
. . 737
14.6.5
The Single-Input Single-Output Solution
........742
14.7
k
Optimal Control:
SISO
Case
.................747
14.8
Exercises
..............................755
14.9
Notes and References
.......................757
15
Яоо
OPTIMAL
MULTIVARIABLE
CONTROL
759
15.1
Яоо
Optimal Control Using Hankel Theory
.......... 759
15.1.1
Яоо
and Hankel Operators
................ 759
15.1.2
State Space Computations of the Hankel Norm
.... 763
15.1.3
State Space Computation of an All-Pass Extension
. . 769
15.1.4
Яоо
Optimal Control Based on the YJBK
Parametrization and Hankel Approximation Theory
. 771
15.1.5
LQ Return Difference Equality
............. 776
15.1.6
State Space Formulas for
Coprirne
Factorizations
. . . 780
xvi
Linear Control Theory
15.2
The State Space Solution of H^ Optimal Control
.......784
15.2.1
The #oo Solution
.....................784
15.2.2
The H2 Solution
...............*.....795
15.3
Exercises
..............................804
15.4
Notes and References
.......................806
A SIGNAL SPACES
807
A.I Vector Spaces and Norms
....................807
A.
2
Metric Spaces
...........................819
A.3 Equivalent Norms and Convergence
...............825
A.
4
Relations between Normed Spaces
...............828
A.
5
Notes and References
.......................832
В
NORMS FOR LINEAR SYSTEMS
833
B.I Induced Norms for Linear Maps
................. 833
B.2 Properties of Fourier and Laplace Transforms
......... 844
B.2.1 Fourier Transforms
.................... 846
B.2.2 Laplace Transforms
.................... 848
B.3 Lp/lp Norms of Convolutions of Signals
............ 849
B.3.1 L1 Theory
......................... 849
B.3.2 Lp Theory
......................... 850
B.4 Induced Norms of Convolution Maps
.............. 852
B.5 Notes and References
....................... 865
IV EPILOGUE
867
ROBUSTNESS AND FRAGILITY
869
Feedback, Robustness, and Fragility
..................869
Examples
.................................871
Discussion
................................883
Notes and References
..........................885
REFERENCES
887
Index
905
|
| any_adam_object | 1 |
| author | Bhattacharyya, Shankar P. 1946- Datta, Aniruddha 1963- Keel, Lee H. |
| author_GND | (DE-588)121269442 (DE-588)118107526 |
| author_facet | Bhattacharyya, Shankar P. 1946- Datta, Aniruddha 1963- Keel, Lee H. |
| author_role | aut aut aut |
| author_sort | Bhattacharyya, Shankar P. 1946- |
| author_variant | s p b sp spb a d ad l h k lh lhk |
| building | Verbundindex |
| bvnumber | BV035339730 |
| callnumber-first | T - Technology |
| callnumber-label | TJ220 |
| callnumber-raw | TJ220 |
| callnumber-search | TJ220 |
| callnumber-sort | TJ 3220 |
| callnumber-subject | TJ - Mechanical Engineering and Machinery |
| classification_rvk | ZQ 5000 ZQ 5220 ZQ 5222 |
| ctrlnum | (OCoLC)144565585 (DE-599)HBZHT015796895 |
| dewey-full | 629.8/32 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 629 - Other branches of engineering |
| dewey-raw | 629.8/32 |
| dewey-search | 629.8/32 |
| dewey-sort | 3629.8 232 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mess-/Steuerungs-/Regelungs-/Automatisierungstechnik / Mechatronik |
| format | Book |
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| id | DE-604.BV035339730 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:31:38Z |
| institution | BVB |
| isbn | 0849340632 9780849340635 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017144037 |
| oclc_num | 144565585 |
| open_access_boolean | |
| owner | DE-M347 DE-703 DE-706 DE-1050 |
| owner_facet | DE-M347 DE-703 DE-706 DE-1050 |
| physical | XVIII, 911 S. Ill., graph. Darst. 26cm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | CRC Taylor & Francis |
| record_format | marc |
| series | Automation and control engineering |
| series2 | Automation and control engineering |
| spelling | Bhattacharyya, Shankar P. 1946- Verfasser (DE-588)121269442 aut Linear control theory structure, robustness, and optimization Shankar P. Bhattacharyya ; Aniruddha Datta ; L. H. Keel Boca Raton, Fla. CRC 2009 London Taylor & Francis XVIII, 911 S. Ill., graph. Darst. 26cm txt rdacontent n rdamedia nc rdacarrier Automation and control engineering 33 Regelungstheorie Linear control systems Control theory Lineare Regelung (DE-588)4035819-7 gnd rswk-swf Lineare Regelung (DE-588)4035819-7 s DE-604 Datta, Aniruddha 1963- Verfasser (DE-588)118107526 aut Keel, Lee H. Verfasser aut Automation and control engineering 33 (DE-604)BV021743861 33 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017144037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bhattacharyya, Shankar P. 1946- Datta, Aniruddha 1963- Keel, Lee H. Linear control theory structure, robustness, and optimization Automation and control engineering Regelungstheorie Linear control systems Control theory Lineare Regelung (DE-588)4035819-7 gnd |
| subject_GND | (DE-588)4035819-7 |
| title | Linear control theory structure, robustness, and optimization |
| title_auth | Linear control theory structure, robustness, and optimization |
| title_exact_search | Linear control theory structure, robustness, and optimization |
| title_full | Linear control theory structure, robustness, and optimization Shankar P. Bhattacharyya ; Aniruddha Datta ; L. H. Keel |
| title_fullStr | Linear control theory structure, robustness, and optimization Shankar P. Bhattacharyya ; Aniruddha Datta ; L. H. Keel |
| title_full_unstemmed | Linear control theory structure, robustness, and optimization Shankar P. Bhattacharyya ; Aniruddha Datta ; L. H. Keel |
| title_short | Linear control theory |
| title_sort | linear control theory structure robustness and optimization |
| title_sub | structure, robustness, and optimization |
| topic | Regelungstheorie Linear control systems Control theory Lineare Regelung (DE-588)4035819-7 gnd |
| topic_facet | Regelungstheorie Linear control systems Control theory Lineare Regelung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017144037&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021743861 |
| work_keys_str_mv | AT bhattacharyyashankarp linearcontroltheorystructurerobustnessandoptimization AT dattaaniruddha linearcontroltheorystructurerobustnessandoptimization AT keelleeh linearcontroltheorystructurerobustnessandoptimization |