Learn · Nonlinear System Analysis
Lecture 16 of 51Week 6
Phase portrait of Nonlinear Systems: Examples
Prof. Ramkrishna PasumarthyProf. Arunkumar D Mahindrakar · IIT Madras
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- Nonlinear System Analysis, IIT Madras (at NPTEL)
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All the lectures
- Examples of Nonlinear Physical Systems
- Math Preliminaries- Part 01
- Math Preliminaries- Part 02
- Math Preliminaries- Part 03
- Lipschitz Continuity and Contraction Mapping Theorem-Part 01
- Lipschitz Continuity and Contraction Mapping Theorem-Part 02
- Lipschitz Continuity and Contraction Mapping Theorem-Part 03
- Existence and Uniqueness Theorem of ODE.-Part 01
- Existence and Uniqueness Theorem of ODE.-Part 02
- Existence and Uniqueness Theorem of ODE.-Part 03
- Existence and Uniqueness Theorem of ODE.-Part 04
- Equilibrium Points
- Phase Portrait - Part 01
- Phase Portrait - Part 02
- Phase Portrait - Part 03
- Phase portrait of Nonlinear Systems: Examples
- Limit Cycles
- Limit Cycles- Examples (Part 1)
- Limit Cycles- Examples (Part 2)
- Introduction to Bifurcation Theory 1
- Introduction to Bifurcation Theory 2
- Necessary and Sufficient Conditions for Local Bifurcation.
- Problems on Bifurcation Theory.
- Stability Notions: Lyapunov and LaSalle's theorem-Part 01
- Stability Notions: Lyapunov and LaSalle's theorem-Part 02
- Stability Notions: Lyapunov and LaSalle's theorem-Part 03
- Stability Notions: Lyapunov and LaSalle's theorem-Part 04
- Stability Analysis and types of stability
- Lypaunov Stability
- Supplementary lecture: Comparison Lemma and Lyapunov Stability
- Center Manifold Theorem
- Interconnection between non linearity and a linear system - Sector Nonlinearities And Aizermann's conjecture
- Counter example for Aizermann's conjecture
- Passivity inspiration - passive circuits - dissipation equality
- Dissipative Equality for circuit(contn'd)
- PR condition for passivity of SISO system
- Examples of PR transfer functions
- Relation between storage function and Lyapunov function - PR Lemma
- Proof of PR Lemma
- Proof (contn'd) using spectral factorization theorem
- PR definition for MIMO case
- PSD Storage function in PR Lemma and how to make it PD (strictly PR)
- KYP Theorem
- Passivity preservation under interconnection
- Aizermann's conjecture under passivity assumption is true
- Sector Nonlinearities and need for generlaizing KYP Lemma
- Need for Loop transformations
- Loop Transformations (Part 1)
- Loop Transformations (Part 2)
- Circle criterion for PR
- Examples based on circle criterion and stability under circle transformations