SC301 – LINEAR AND NONLINEAR SYSTEMS
Course offered in:
2019-2020
Instructors:
Prof. Srikant Sukumar and Prof. Arpita Sinha
Course Content:
The course was divided into 2 parts –
- Linear Systems
- Non-Linear Systems
Topics covered in Part 1 – ODE existence and uniqueness, State transition matrix properties, Jordan decomposition, Controllability, Observability, Lyapunov functions for stability analysis, Specialization to eigenvalues for LTI case, Linear feedback – LTI pole placement via canonical forms, LQR, Output feedback.
Topics covered in Part 2 – Local/global existence and uniqueness of solutions to nonlinear ODE’s, Lyapunov stability definitions, linearizing of non-linear systems, Phase Space Plots, equilibrium points, identifying uniform stability, uniform asymptotic stability, exponential stability and global stability, Lyapunov direct method, Lyapunov theorems for stability, Krasovskii-LaSalle theorem.
Prerequisites:
SC201 (or SC639), SC202
Feedback on Lectures:
Prof. Srikant taught us part 1 and Prof. Sinha taught us part 2. Their teaching styles were quite different but both of them always interacted with the students and answered doubts satisfactorily. Srikant sir is an amazing teacher and his lectures were always fun to attend. He used to bring his handwritten notes and project them a screen. Any mistake in the notes was recognized and corrected promptly and the final version was uploaded on moodle. The only difficulty I faced in his lectures was his fast pace. Arpita ma’am preferred using the board so we had to make our own notes. She always took some time to answer questions but made sure that all doubts were cleared. She is a decent teacher but I personally found her lectures slightly boring.
A lot of content was covered in a very short time so it was crucial to attend lectures and study the concepts regularly.
Feedback on Tutorials, Assignments and Exams:
Grading scheme –
Part 1
Best of Quiz 1 and Quiz 2 – 25%
Midsem – 25%
Part 2
Quiz 1 – 25 %
Endsem – 25 %
All exams were open book and open notes and therefore quite difficult. Tutorials were conducted occasionally where we solved some problems and and asked our doubts.
Difficulty:
(on a scale of 1 being very easy to 5 being very hard): 4
Grading Statistics:
AA 2
AB 4
AP 1
BB 4
BC 5
CC 1
FR 2
W 1
Total 20
Study Material and References:
- Linear System Theory by Joao P. Hespanha
- Linear Systems by Panos J. Antsaklis, Anthony N. Michel
- Nonlinear Systems by Hassan Khalil
- Nonlinear Systems Analysis, Volume 42 of Classics in Applied Mathematics, M. Vidyasagar
Takeaways from the course:
This is the 3rd core course of SysCon Minor. Completing this course will allow you to purse more advanced courses of in Control Theory.