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