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Course10810616251 lectures

Nonlinear System Analysis

Prof. Ramkrishna PasumarthyProf. Arunkumar D Mahindrakar · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Week 1

  1. Examples of Nonlinear Physical Systems Video

Week 2

  1. Math Preliminaries- Part 01 Video
  2. Math Preliminaries- Part 02 Video
  3. Math Preliminaries- Part 03 Video

Week 3

  1. Lipschitz Continuity and Contraction Mapping Theorem-Part 01 Video
  2. Lipschitz Continuity and Contraction Mapping Theorem-Part 02 Video
  3. Lipschitz Continuity and Contraction Mapping Theorem-Part 03 Video

Week 4

  1. Existence and Uniqueness Theorem of ODE.-Part 01 Video
  2. Existence and Uniqueness Theorem of ODE.-Part 02 Video
  3. Existence and Uniqueness Theorem of ODE.-Part 03 Video
  4. Existence and Uniqueness Theorem of ODE.-Part 04 Video

Week 5

  1. Equilibrium Points Video
  2. Phase Portrait - Part 01 Video
  3. Phase Portrait - Part 02 Video
  4. Phase Portrait - Part 03 Video

Week 6

  1. Phase portrait of Nonlinear Systems: Examples Video
  2. Limit Cycles Video
  3. Limit Cycles- Examples (Part 1) Video
  4. Limit Cycles- Examples (Part 2) Video

Week 7

  1. Introduction to Bifurcation Theory 1 Video
  2. Introduction to Bifurcation Theory 2 Video
  3. Necessary and Sufficient Conditions for Local Bifurcation. Video
  4. Problems on Bifurcation Theory. Video

Week 8

  1. Stability Notions: Lyapunov and LaSalle's theorem-Part 01 Video
  2. Stability Notions: Lyapunov and LaSalle's theorem-Part 02 Video
  3. Stability Notions: Lyapunov and LaSalle's theorem-Part 03 Video
  4. Stability Notions: Lyapunov and LaSalle's theorem-Part 04 Video

Week 9

  1. Stability Analysis and types of stability Video
  2. Lypaunov Stability Video
  3. Supplementary lecture: Comparison Lemma and Lyapunov Stability Video
  4. Center Manifold Theorem Video

Week 10

  1. Interconnection between non linearity and a linear system - Sector Nonlinearities And Aizermann's conjecture Video
  2. Counter example for Aizermann's conjecture Video
  3. Passivity inspiration - passive circuits - dissipation equality Video
  4. Dissipative Equality for circuit(contn'd) Video
  5. PR condition for passivity of SISO system Video

Week 11

  1. Examples of PR transfer functions Video
  2. Relation between storage function and Lyapunov function - PR Lemma Video
  3. Proof of PR Lemma Video
  4. Proof (contn'd) using spectral factorization theorem Video
  5. PR definition for MIMO case Video
  6. PSD Storage function in PR Lemma and how to make it PD (strictly PR) Video
  7. KYP Theorem Video
  8. Passivity preservation under interconnection Video
  9. Aizermann's conjecture under passivity assumption is true Video

Week 12

  1. Sector Nonlinearities and need for generlaizing KYP Lemma Video
  2. Need for Loop transformations Video
  3. Loop Transformations (Part 1) Video
  4. Loop Transformations (Part 2) Video
  5. Circle criterion for PR Video
  6. Examples based on circle criterion and stability under circle transformations Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Electrical Engineering
Teacher
Prof. Ramkrishna PasumarthyProf. Arunkumar D Mahindrakar
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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