Nonlinear System Analysis

Nonlinear System Analysis

@VTU COE

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What you will learn

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All systems are inherently nonlinear in nature. This course deals with the analysis of nonlinear systems. The need for special tools to analyze nonlinear systems arises from the fact that the principle of superposition on which linear analysis is based, fails in the nonlinear case. The course exposes the students to various tools to analyze the behaviour of nonlinear systems, culminating in the stability analysis, which is of paramount importance in control systems.

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Math Preliminaries- Part 01
Preview 40:00
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Math Preliminaries- Part 02
Preview 35:58
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Math Preliminaries- Part 03
Preview 34:16

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Lipschitz Continuity and Contraction Mapping Theorem-Part 01
Preview 12:00
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Lipschitz Continuity and Contraction Mapping Theorem-Part 02
Preview 19:08
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Lipschitz Continuity and Contraction Mapping Theorem-Part 03
Preview 18:15

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Existence and Uniqueness Theorem of ODE.-Part 01
Preview 18:18
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Existence and Uniqueness Theorem of ODE.-Part 02
Preview 17:52
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Existence and Uniqueness Theorem of ODE.-Part 03
Preview 12:11
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Existence and Uniqueness Theorem of ODE.-Part 04
Preview 16:17

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Equilibrium Points
Preview 49:19
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Phase Portrait - Part 01
Preview 18:10
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Phase Portrait - Part 02
Preview 51:06
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Phase Portrait - Part 03
Preview 40:51

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Phase portrait of Nonlinear Systems: Examples
Preview 33:50
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Limit Cycles
Preview 20:01
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Limit Cycles- Examples (Part 1)
Preview 23:30
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Limit Cycles- Examples (Part 2)
Preview 36:16

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Introduction to Bifurcation Theory 1
Preview 36:37
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Introduction to Bifurcation Theory 2
Preview 41:10
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Necessary and Sufficient Conditions for Local Bifurcation.
Preview 50:00
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Problems on Bifurcation Theory.
Preview 46:07

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Stability Notions: Lyapunov and LaSalle's theorem-Part 01
Preview 25:45
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Stability Notions: Lyapunov and LaSalle's theorem-Part 02
Preview 54:12
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Stability Notions: Lyapunov and LaSalle's theorem-Part 03
Preview 55:35
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Stability Notions: Lyapunov and LaSalle's theorem-Part 04
Preview 34:47

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Stability Analysis and types of stability
Preview 28:33
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Lypaunov Stability
Preview 64:09
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Supplementary lecture: Comparison Lemma and Lyapunov Stability
Preview 28:00
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Center Manifold Theorem
Preview 37:39

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Interconnection between non linearity and a linear system - Sector Nonlinearities And Aizermann's conjecture
Preview 19:27
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Counter example for Aizermann's conjecture
Preview 14:00
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Passivity inspiration - passive circuits - dissipation equality
Preview 18:55
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Dissipative Equality for circuit(contn'd)
Preview 05:07
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PR condition for passivity of SISO system
Preview 10:26

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Examples of PR transfer functions
Preview 10:00
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Relation between storage function and Lyapunov function - PR Lemma
Preview 22:27
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Proof of PR Lemma
Preview 26:56
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Proof (contn'd) using spectral factorization theorem
Preview 25:27
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PR definition for MIMO case
Preview 19:27
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PSD Storage function in PR Lemma and how to make it PD (strictly PR)
Preview 07:29
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KYP Theorem
Preview 03:05
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Passivity preservation under interconnection
Preview 12:06
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Aizermann's conjecture under passivity assumption is true
Preview 10:16

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Sector Nonlinearities and need for generlaizing KYP Lemma
Preview 23:43
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Need for Loop transformations
Preview 11:00
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Loop Transformations (Part 1)
Preview 19:52
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Loop Transformations (Part 2)
Preview 33:17
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Circle criterion for PR
Preview 16:03
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Examples based on circle criterion and stability under circle transformations
Preview 56:09
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Meet Your Instructor
@VTU COE
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Instructor
3.2 Rating
2542 Students
759 Courses
About Instructor

VTU is one of the largest Technological Universities in India with 24 years of Tradition of excellence in Engineering & Technical Education, Research and Innovations. It came into existence in the year 1998 to cater the needs of Indian industries for trained technical manpower with practical experience and sound theoretical knowledge.

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Free

  • Course Duration
    23 h 23 m 10 s
  • Course Level
    Intermediate
  • Student Enrolled
    0
  • Language
    English
This Course Includes
  • 23 h 23 m 10 s Video Lectures
  • 0 Quizzes
  • 0 Assignments
  • 0 Downloadable Resources
  • Full Lifetime Access
  • Certificate of Completion