Nonlinear System Analysis

By Prof. Ramkrishna Pasumarthy, Prof. Arunkumar D Mahindrakar   |   IIT Madras
Learners enrolled: 357
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.

INTENDED AUDIENCE :PhD, MS/M. Tech/ ME, Senior Undergraduate students from EE, ME, AE, PH 
PRE- REQUISITES : Undergrad control engineering, basic knowledge of differential equations and linear algebra is highly desirable.
SUPPORT INDUSTRY : Any robotics, space and defence related industries
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Electrical, Electronics and Communications Engineering
  • Control and Instrumentation
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 24 Jan 2022
End Date : 15 Apr 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 24 Apr 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 : Why nonlinear systems? - Non-linear Models of Physical Systems 
Week 2 : Mathematical Preliminaries: Finite dimensional normed spaces, Euclidean space and its topology 
Week 3 : Infinite dimensional Banach spaces - Contraction mapping theorem
Week 4 : Existence and Uniqueness results for solutions to non linear ODEs 
Week 5 : ODEs as vector fields - One dimensional systems - Phase portrait of second order linear systems - 
    Equilibrium points, linearization and their classification
Week 6 : Examples: Simple pendulum, Bead on a hoop, Lotka-Volterra models for predation and competition, 
          biological transcriptional system, van der Pol oscillator and conservative systems, non linear circuits - Limit cycles
Week 7 : Bifurcations of two dimensional flows: Saddle-node, pitchfork, transcritical and Hopf - their normal forms
Week 8 : Notions of stability - Lyapunov and LaSalle’s theorems
Week 9 : Finding Lyapunov functions: Linear systems, variable gradient method - Center Manifold Theorem
Week 10 : Physical Non-linearities - Interconnections and feedback - Aizermann’s conjecture - Passivity
Week 11 : PR systems - Dissipation equality - Passive filters
Week 12 : KYP Lemma - Popov and circle criterion

Books and references

1.Nonlinear Systems - Hassan Khalil
2.Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering - Steven Strogatz
3.Nonlinear systems: analysis, stability, and control - S.S.Sastry
4.Nonlinear Systems Analysis - Vidyasagar

Instructor bio

Prof. Ramkrishna Pasumarthy

IIT Madras
Ramkrishna Pasumarthy is an Associate Professor at the Dept. of Electrical Engineering, IIT Madras. He obtained his PhD in Systems and Control at the University of Twente, The Netherlands and held postdoc positions at the University of Melbourne and UCLA. He held visiting positions at Stanford University. His research interests are in the areas of network science with applications to power, traffic cloud and brain networks. also associated with the Robert Bosch Center for Data Sciences and Artificial Intelligence at IIT Madras. He also has interests in medical wearable devices and is a co funder of a start up iMov Motion Tech pvt. ltd. incubated at IITM Research Park

Prof. Arunkumar D Mahindrakar

1. Arun Mahindrakar is an Associate Professor in the Department of Electrical Engineering, IIT Madras. He received his Ph.D. degree in Systems and Control from IIT Bombay, Mumbai, India, in 2004. He was a Postdoctoral Fellow with the Laboratory of Signals and Systems, Supelec, Paris, France, from 2004 to 2005. His research interests include nonlinear stability, geometric control, and formation control of multiagent systems.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 April 2022 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.


Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Madras .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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