NOC:Nonlinear System Analysis


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