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ÃÎÃÈÒÐ(½ð±Ò+2):±à¼­¹¦ÄÜλÓÚÿһ¥ÓÒϽǴ¦¡£ÁíÍ⣬ÒòΪÊÇг棬ËùÒÔ×·¼Ó½±Àø£¬Ï£Íû³£À´¡£ 2010-05-22 17:19:57
Building Uncertain Models
Introduction to Uncertain Atoms . . . . . . . . . . . . . . . . . . . . . . . 1-2
Uncertain Real Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3
Uncertain LTI Dynamics Atoms . . . . . . . . . . . . . . . . . . . . . . . . 1-10
Complex Parameter Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-13
Complex Matrix Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-15
Unstructured Uncertain Dynamic Systems . . . . . . . . . . . . . . . 1-17
Uncertain Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-19
Creating Uncertain Matrices from Uncertain Atoms . . . . . . . 1-19
Accessing Properties of a umat . . . . . . . . . . . . . . . . . . . . . . . . . 1-20
Row and Column Referencing . . . . . . . . . . . . . . . . . . . . . . . . . . 1-21
Matrix Operation on umat Objects . . . . . . . . . . . . . . . . . . . . . . 1-22
Substituting for Uncertain Atoms . . . . . . . . . . . . . . . . . . . . . . 1-23
Uncertain State-Space Systems (uss) . . . . . . . . . . . . . . . . . . 1-25
Creating Uncertain Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-25
Properties of uss Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-26
Sampling Uncertain Systems . . . . . . . . . . . . . . . . . . . . . . . . . . 1-27
Feedback Around an Uncertain Plant . . . . . . . . . . . . . . . . . . . 1-28
Interpreting Uncertainty in Discrete Time . . . . . . . . . . . . . . . 1-30
Lifting a ss to a uss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Handling Delays in uss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-31
Uncertain frd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-33
Creating Uncertain Frequency Response Objects . . . . . . . . . . 1-33
Properties of ufrd Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-33
Interpreting Uncertainty in Discrete Time . . . . . . . . . . . . . . . 1-36
Lifting an frd to a ufrd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
Handling Delays in ufrd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-36
Basic Control System Toolbox™ and
MATLAB® Interconnections . . . . . . . . . . . . . . . . . . . . . . . . . . 1-37
Simplifying Representation of Uncertain Objects . . . . . . . 1-38
vi Contents
Effect of the Autosimplify Property . . . . . . . . . . . . . . . . . . . . . 1-39
Direct Use of simplify . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-41
Sampling Uncertain Objects . . . . . . . . . . . . . . . . . . . . . . . . . . 1-42
Generating One Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-42
Generating Many Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-42
Sampling ultidyn Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-43
Substitution by usubs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-46
Specifying the Substitution with Structures . . . . . . . . . . . . . . 1-47
Nominal and Random Values . . . . . . . . . . . . . . . . . . . . . . . . . . 1-47
Array Management for Uncertain Objects . . . . . . . . . . . . . . 1-49
Referencing Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-49
Creating Arrays with stack and cat Functions . . . . . . . . . . . . 1-50
Creating Arrays by Assignment . . . . . . . . . . . . . . . . . . . . . . . . 1-52
Binary Operations with Arrays . . . . . . . . . . . . . . . . . . . . . . . . . 1-53
Creating Arrays with usample . . . . . . . . . . . . . . . . . . . . . . . . . 1-53
Creating Arrays with usubs . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-55
Creating Arrays with gridureal . . . . . . . . . . . . . . . . . . . . . . . . . 1-56
Creating Arrays with repmat . . . . . . . . . . . . . . . . . . . . . . . . . . 1-57
Creating Arrays with repsys . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-58
Using permute and ipermute . . . . . . . . . . . . . . . . . . . . . . . . . . 1-58
Decomposing Uncertain Objects (for Advanced Users) . . 1-60
Normalizing Functions for Uncertain Atoms . . . . . . . . . . . . . . 1-60
Properties of the Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 1-61
Syntax of lftdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-62
Advanced Syntax of lftdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-64
2
Generalized Robustness Analysis
Introduction to Generalized Robustness Analysis . . . . . . . . 2-2
Robust Stability Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-4
vii
Robust Performance Margin . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
Worst-Case Gain Measure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
3
Introduction to Linear Matrix Inequalities
Linear Matrix Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
LMI Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
LMIs and LMI Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-4
Three Generic LMI Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
Further Mathematical Background . . . . . . . . . . . . . . . . . . . . . 3-9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-10
4
LMI Lab
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
Overview of the LMI Lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
Specifying a System of LMIs . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7
A Simple Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-8
Initializing the LMI System . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10
Specifying the LMI Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10
Specifying Individual LMIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-13
Specifying LMIs with the LMI Editor . . . . . . . . . . . . . . . . . . . . 4-15
How It All Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-19
Querying the LMI System Description . . . . . . . . . . . . . . . . . 4-20
lmiinfo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20
viii Contents
lminbr and matnbr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20
LMI Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21
From Decision to Matrix Variables and Vice Versa . . . . . . 4-27
Validating Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-28
Modifying a System of LMIs . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29
Deleting an LMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29
Deleting a Matrix Variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-29
Instantiating a Matrix Variable . . . . . . . . . . . . . . . . . . . . . . . . 4-30
Advanced Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32
Structured Matrix Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-32
Complex-Valued LMIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-34
Specifying cTx Objectives for mincx . . . . . . . . . . . . . . . . . . . . . 4-37
Feasibility Radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-38
Well-Posedness Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-39
Semi-Definite B(x) in gevp Problems . . . . . . . . . . . . . . . . . . . . 4-40
Efficiency and Complexity Issues . . . . . . . . . . . . . . . . . . . . . . . 4-41
Solving M + PTXQ + QTXTP < 0 . . . . . . . . . . . . . . . . . . . . . . . . 4-41
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-43
5
Function Reference
Functions ¡ª By Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
Uncertain Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Uncertain Matrices and Systems . . . . . . . . . . . . . . . . . . . . . . . . 5-4
Manipulation of Uncertain Models . . . . . . . . . . . . . . . . . . . . . . . 5-4
Interconnection of Uncertain Models . . . . . . . . . . . . . . . . . . . . . 5-6
Model Order Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-6
Robustness and Worst-Case Analysis . . . . . . . . . . . . . . . . . . . . . 5-7
Robustness Analysis for Parameter-Dependent
Systems (P-Systems) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
ix
Controller Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
¦Ì-Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Sampled-Data Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Gain Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-10
Frequency-Response Data (FRD) Models . . . . . . . . . . . . . . . . . 5-10
Supporting Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12
LMIs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12
Functions ¡ª Alphabetical List . . . . . . . . . . . . . . . . . . . . . . . . 5-15
6
Block Reference
Index
2Â¥2010-05-22 16:35:49
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ÒýÓûØÌû:
1Â¥: Originally posted by bitqf168 at 2010-05-20 23:59:44:
Ò×ÅÌÏÂÔØ:
https://www.163pan.com/files/80d000z0u.html
ÎļþÃû³Æ:
        MATLAB7.8³°ô¿ØÖƱ¦µä.pdf
==============================
[ Last edited by ÷ÈôÃù on 2010-5-21 at 09:31 ]

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