# Nonlinear System Analysis - Institution: IIT Madras - Department: Electrical Engineering - Teacher: Prof. Ramkrishna PasumarthyProf. Arunkumar D Mahindrakar - Level: Undergraduate - Language: English - Subjects: Engineering - Source: [NPTEL](https://nptel.ac.in/courses/108106162) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/108106162) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) ## Lectures 1. [Examples of Nonlinear Physical Systems](https://invisiblenetwork.ai/learn/nptel/108106162/d59016ea4889) (Video) 2. [Math Preliminaries- Part 01](https://invisiblenetwork.ai/learn/nptel/108106162/34c0a1d58f27) (Video) 3. [Math Preliminaries- Part 02](https://invisiblenetwork.ai/learn/nptel/108106162/0f6c542004a8) (Video) 4. [Math Preliminaries- Part 03](https://invisiblenetwork.ai/learn/nptel/108106162/3628e768d2dc) (Video) 5. [Lipschitz Continuity and Contraction Mapping Theorem-Part 01](https://invisiblenetwork.ai/learn/nptel/108106162/5f63f7c6d755) (Video) 6. [Lipschitz Continuity and Contraction Mapping Theorem-Part 02](https://invisiblenetwork.ai/learn/nptel/108106162/141ebf7bd767) (Video) 7. [Lipschitz Continuity and Contraction Mapping Theorem-Part 03](https://invisiblenetwork.ai/learn/nptel/108106162/a1768f755253) (Video) 8. [Existence and Uniqueness Theorem of ODE.-Part 01](https://invisiblenetwork.ai/learn/nptel/108106162/a4a8ca1a9066) (Video) 9. [Existence and Uniqueness Theorem of ODE.-Part 02](https://invisiblenetwork.ai/learn/nptel/108106162/603993d626a4) (Video) 10. [Existence and Uniqueness Theorem of ODE.-Part 03](https://invisiblenetwork.ai/learn/nptel/108106162/3654bdedce9d) (Video) 11. [Existence and Uniqueness Theorem of ODE.-Part 04](https://invisiblenetwork.ai/learn/nptel/108106162/7dd2d05dd997) (Video) 12. [Equilibrium Points](https://invisiblenetwork.ai/learn/nptel/108106162/36cc4d74da40) (Video) 13. [Phase Portrait - Part 01](https://invisiblenetwork.ai/learn/nptel/108106162/21ebffc5c96c) (Video) 14. [Phase Portrait - Part 02](https://invisiblenetwork.ai/learn/nptel/108106162/81dcacb57621) (Video) 15. [Phase Portrait - Part 03](https://invisiblenetwork.ai/learn/nptel/108106162/f33f834a1145) (Video) 16. [Phase portrait of Nonlinear Systems: Examples](https://invisiblenetwork.ai/learn/nptel/108106162/234f05bc576c) (Video) 17. [Limit Cycles](https://invisiblenetwork.ai/learn/nptel/108106162/1f937de2dc8b) (Video) 18. [Limit Cycles- Examples (Part 1)](https://invisiblenetwork.ai/learn/nptel/108106162/1665606d19eb) (Video) 19. [Limit Cycles- Examples (Part 2)](https://invisiblenetwork.ai/learn/nptel/108106162/301490765f0b) (Video) 20. [Introduction to Bifurcation Theory 1](https://invisiblenetwork.ai/learn/nptel/108106162/06d6357e9e11) (Video) 21. [Introduction to Bifurcation Theory 2](https://invisiblenetwork.ai/learn/nptel/108106162/da7ed5b482b1) (Video) 22. [Necessary and Sufficient Conditions for Local Bifurcation.](https://invisiblenetwork.ai/learn/nptel/108106162/694f1792c542) (Video) 23. [Problems on Bifurcation Theory.](https://invisiblenetwork.ai/learn/nptel/108106162/ed8ddeb81e67) (Video) 24. [Stability Notions: Lyapunov and LaSalle's theorem-Part 01](https://invisiblenetwork.ai/learn/nptel/108106162/a94ea26e0b9f) (Video) 25. [Stability Notions: Lyapunov and LaSalle's theorem-Part 02](https://invisiblenetwork.ai/learn/nptel/108106162/22253167583f) (Video) 26. [Stability Notions: Lyapunov and LaSalle's theorem-Part 03](https://invisiblenetwork.ai/learn/nptel/108106162/6cb68eb04698) (Video) 27. [Stability Notions: Lyapunov and LaSalle's theorem-Part 04](https://invisiblenetwork.ai/learn/nptel/108106162/430abfc22af4) (Video) 28. [Stability Analysis and types of stability](https://invisiblenetwork.ai/learn/nptel/108106162/2e5aff12bb56) (Video) 29. [Lypaunov Stability](https://invisiblenetwork.ai/learn/nptel/108106162/7f4f6b83ea7c) (Video) 30. [Supplementary lecture: Comparison Lemma and Lyapunov Stability](https://invisiblenetwork.ai/learn/nptel/108106162/bd47ba8d8917) (Video) 31. [Center Manifold Theorem](https://invisiblenetwork.ai/learn/nptel/108106162/6e7152d20d3c) (Video) 32. [Interconnection between non linearity and a linear system - Sector Nonlinearities And Aizermann's conjecture](https://invisiblenetwork.ai/learn/nptel/108106162/3fd9943e11f3) (Video) 33. [Counter example for Aizermann's conjecture](https://invisiblenetwork.ai/learn/nptel/108106162/1ab515659524) (Video) 34. [Passivity inspiration - passive circuits - dissipation equality](https://invisiblenetwork.ai/learn/nptel/108106162/bcb6681d6199) (Video) 35. [Dissipative Equality for circuit(contn'd)](https://invisiblenetwork.ai/learn/nptel/108106162/4ce2a2b63b35) (Video) 36. [PR condition for passivity of SISO system](https://invisiblenetwork.ai/learn/nptel/108106162/a26c2b6d5b1a) (Video) 37. [Examples of PR transfer functions](https://invisiblenetwork.ai/learn/nptel/108106162/baeb50b01a0b) (Video) 38. [Relation between storage function and Lyapunov function - PR Lemma](https://invisiblenetwork.ai/learn/nptel/108106162/3e99b114582f) (Video) 39. [Proof of PR Lemma](https://invisiblenetwork.ai/learn/nptel/108106162/72b6ded22f07) (Video) 40. [Proof (contn'd) using spectral factorization theorem](https://invisiblenetwork.ai/learn/nptel/108106162/0df6e403dc7e) (Video) 41. [PR definition for MIMO case](https://invisiblenetwork.ai/learn/nptel/108106162/1c0dc9685879) (Video) 42. [PSD Storage function in PR Lemma and how to make it PD (strictly PR)](https://invisiblenetwork.ai/learn/nptel/108106162/80ddff602d47) (Video) 43. [KYP Theorem](https://invisiblenetwork.ai/learn/nptel/108106162/daaa68aef172) (Video) 44. [Passivity preservation under interconnection](https://invisiblenetwork.ai/learn/nptel/108106162/51d188f84151) (Video) 45. [Aizermann's conjecture under passivity assumption is true](https://invisiblenetwork.ai/learn/nptel/108106162/255f204cc2f1) (Video) 46. [Sector Nonlinearities and need for generlaizing KYP Lemma](https://invisiblenetwork.ai/learn/nptel/108106162/79d27fac073c) (Video) 47. [Need for Loop transformations](https://invisiblenetwork.ai/learn/nptel/108106162/8414793d45e4) (Video) 48. [Loop Transformations (Part 1)](https://invisiblenetwork.ai/learn/nptel/108106162/806fff6fb7b0) (Video) 49. [Loop Transformations (Part 2)](https://invisiblenetwork.ai/learn/nptel/108106162/a0b39a9a62db) (Video) 50. [Circle criterion for PR](https://invisiblenetwork.ai/learn/nptel/108106162/65e74ccdbd5a) (Video) 51. [Examples based on circle criterion and stability under circle transformations](https://invisiblenetwork.ai/learn/nptel/108106162/27b6595551bc) (Video)