Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Dr. Arun D. Mahindrakar, Prof. Ramkrishna Pasumarthy
NPTEL Co-ordinating Institute : IIT Madras
NPTEL Lecture Count : 51
NPTEL Course Size : 19 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Examples of Nonlinear Physical Systems
Lecture 2 - Math Preliminaries - Part 1
Lecture 3 - Math Preliminaries - Part 2
Lecture 4 - Math Preliminaries - Part 3
Lecture 5 - Lipschitz Continuity and Contraction Mapping Theorem - Part 1
Lecture 6 - Lipschitz Continuity and Contraction Mapping Theorem - Part 2
Lecture 7 - Lipschitz Continuity and Contraction Mapping Theorem - Part 3
Lecture 8 - Existence and Uniqueness Theorem of ODE - Part 1
Lecture 9 - Existence and Uniqueness Theorem of ODE - Part 2
Lecture 10 - Existence and Uniqueness Theorem of ODE - Part 3
Lecture 11 - Existence and Uniqueness Theorem of ODE - Part 4
Lecture 12 - Equilibrium Points
Lecture 13 - Phase Portrait - Part 1
Lecture 14 - Phase Portrait - Part 2
Lecture 15 - Phase Portrait - Part 3
Lecture 16 - Phase portrait of Nonlinear Systems: Examples
Lecture 17 - Limit Cycles
Lecture 18 - Limit Cycles - Examples - Part 1
Lecture 19 - Limit Cycles - Examples - Part 2
Lecture 20 - Introduction to Bifurcation Theory - 1
Lecture 21 - Introduction to Bifurcation Theory - 2
Lecture 22 - Necessary and Sufficient Conditions for Local Bifurcation
Lecture 23 - Problems on Bifurcation Theory.
Lecture 24 - Stability Notions: Lyapunov and LaSalle's theorem - Part 1
Lecture 25 - Stability Notions: Lyapunov and LaSalle's theorem - Part 2
Lecture 26 - Stability Notions: Lyapunov and LaSalle's theorem - Part 3
Lecture 27 - Stability Notions: Lyapunov and LaSalle's theorem - Part 4
Lecture 28 - Stability Analysis and types of stability
Lecture 29 - Lypaunov Stability
Lecture 30 - Supplementary lecture: Comparison Lemma and Lyapunov Stability
Lecture 31 - Center Manifold Theorem
Lecture 32 - Interconnection between non linearity and a linear system - Sector Nonlinearities And Aizermann’s conjecture
Lecture 33 - Counter example for Aizermann’s conjecture
Lecture 34 - Passivity inspiration - passive circuits - dissipation equality
Lecture 35 - Dissipative Equality for circuit (Continued...)
Lecture 36 - PR condition for passivity of SISO system
Lecture 37 - Examples of PR transfer functions
Lecture 38 - Relation between storage function and Lyapunov function - PR Lemma
Lecture 39 - Proof of PR Lemma
Lecture 40 - Proof (Continued...) using spectral factorization theorem
Lecture 41 - PR definition for MIMO case
Lecture 42 - PSD Storage function in PR Lemma and how to make it PD (strictly PR)
Lecture 43 - KYP Theorem
Lecture 44 - Passivity preservation under interconnection
Lecture 45 - Aizermann’s conjecture under passivity assumption is true
Lecture 46 - Sector Nonlinearities and need for generlaizing KYP Lemma
Lecture 47 - Need for Loop transformations
Lecture 48 - Loop Transformations - Part 1
Lecture 49 - Loop Transformations - Part 2
Lecture 50 - Circle criterion for PR
Lecture 51 - Examples based on circle criterion and stability under circle transformations