Sections 3.2, 3.2, 3.4 Dependence on Data, Sensitivity ...

Nonlinear Systems Analysis

Lecture 7

Sections 3.2, 3.2, 3.4

Dependence on Data, Sensitivity Analysis,

Comparison Principle

Feng-Li LianNTU-EE

Sep04 – Jan05

Ch3B-2

Outline

Introduction (L5)

Banach Space (L5)

Contraction Mapping Theorem (L5)

Existence and Uniqueness (L6)

Continuous Dependence on Initial Conditions and Parameters (L6)

Differentiability of Solutions and Sensitivity Equations (L7)

Comparison Principle (L7)

Ch3B-3

Continuous Dependence on Data - 1 (3.2)

Ch3B-4

Continuous Dependence on Data - 2

Ch3B-5

Continuous Dependence on Data - 3

Ch3B-6

Gronwall-Bellman Inequality - 1 (App. A, page 651)

Ch3B-7

Gronwall-Bellman Inequality - 2

Ch3B-8

Closeness of Solutions - 1 (3.2)

Ch3B-9

Closeness of Solutions - 2

Ch3B-10

Ch3B-11

Ch3B-12

Dependence on Initial States & Parameters - 1 (3.2)

Ch3B-13

Dependence on Initial States & Parameters - 2

Ch3B-14

Ch3B-15

Ch3B-16

Ch3B-17

Ch3B-18

Ch3B-19

Differentiability of Solutions - 1 (3.3)

Ch3B-20

Differentiability of Solutions - 2

Ch3B-21

Differentiability of Solutions - 3

Ch3B-22

Sensitivity Equation - 1 (3.3)

Ch3B-23

Sensitivity Equation - 2

Ch3B-24

Sensitivity Equation - 3

Ch3B-25

Comparison Principle - 1 (3.4)

Ch3B-26

Comparison Principle - 2

Ch3B-27

Comparison Principle - 3

Ch3B-28

Example 3.8 - 1 (3.4)

Ch3B-29

Example 3.8 - 2

Sections 3.2, 3.2, 3.4 Dependence on Data, Sensitivity ...

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