Linear Dynamical Systems

By Prof. Tushar Jain   |   IIT Mandi
Learners enrolled: 372
Linear system is the cornerstone of control theory and a prerequisite subject for almost all advanced level graduate courses in this area. The aim of this course is to take a beginning student, with some prior exposure to elementary transform and linear algebra, through a motivated and integrated development of the fuller perspective of the linear system theory. This course will also strengthen the basic logical arguments behind mathematical proofs.

INTENDED AUDIENCE UG, PG Students and Industry Personnel.
RE-REQUISITES : UG control systems, basics of linear algebra
Robotics/Mechatronics (e.g. ABB), Automation Sector (e.g. Honeywell Automation, Robert Bosch Ltd.), Process Industries (e.g. ACC Ltd.)
Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Electrical, Electronics and Communications Engineering
  • Multidisciplinary
  • Control and Instrumentation
Credit Points : 2
Level : Postgraduate
Start Date : 24 Jan 2022
End Date : 18 Mar 2022
Enrollment Ends : 07 Feb 2022
Exam Date : 27 Mar 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: State-space solutions and realizations
Week 2: Stability
Week 3: Controllability: Part I
Week 4: Controllability: Part II
Week 5: State Feedback Controller Design: Part I
Week 6: State Feedback Controller Design: Part II
Week 7: Observability and minimal realization
Week 8: Observer Design and Output Feedback

Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.

Books and references

1.T. Kailath, Linear Systems, Englewood Cliffs, Prentice-Hall, Englewood Cliffs, NJ, 1980
2.P.J. Antsaklis and A.N. Michel, Linear Systems, McGraw-Hill, Englewood Cliffs, NJ, 1997
3.C.T. Chen, Linear System Theory and Design, Oxford University Press, 3rd Edition, 1999
4.J.P. Hespanha, Linear Systems Theory, Princeton University Press, 2009

Instructor bio

Prof. Tushar Jain

IIT Mandi
Dr. Tushar JAIN received the degree of Doctor in Control, Identification and Diagnostic from the Universite de Lorraine, Nancy, France in 2012. He previously received the degree of M.Tech. in System modeling and control from Indian Institute of Technology (IIT) Roorkee in 2009. From 2013 to 2014 and 2014 to 2015, he was a Post-doc researcher and Academy of Finland researcher respectively in the Research Group of Process Control at Aalto University, Finland. Since 2015, he is with the School of Computing and Electrical Engineering, IIT Mandi. During these last years, his research interest has been mainly concentrated on fault tolerant control, fault diagnosis and control for energy-efficient utilisation of renewable energy systems. He has received twice the best paper award for his research work. He has authored a book entitled Active Fault-Tolerant Control Systems: A Behavioral System Theoretic Perspective. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE).

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: 27 March 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 6 assignments out of the total 8 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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