E1 241 - Dynamics of Linear Systems (3:0)

Term & Timing: August - November 2025, Tue and Thurs: 2:00-3:30 PM

First class on 5th August 2025 (Tuesday) 2:00-3:30 PM

Instructors:

Kiran Kumari, Assistant Professor at the Department of Electrical Engineering

Email: kirank@iisc.ac.in 

Teaching Assistants:  

1. Rakshith arakshith@iisc.ac.in

2. Sudhanshu Shekhar sudhanshus1@iisc.ac.in

Venue: B 304, Second Floor, EE Building 

Class Logistics: Registered students will be added to a Class group in Microsoft Teams. The link to join the Teams group is here. All the course correspondence will happen in this Teams group. 

Syllabus: This is an introductory graduate-level course on control system theory. The students will learn analysis, design, and control of physical systems that are dynamic in nature (that is, systems which evolve over time). The course focuses on systems that can be described by linear dynamical equations. There will be a strong emphasis on the mathematical analysis of these systems using tools from linear algebra and matrix theory. The course will enable students to think “mathematically” and apply relevant techniques to derive mathematical results for these systems. 

We will broadly cover the following topics:   

1. State space and input-output descriptions  

2. Time response and asymptotic behavior  

3. Stability   

4. Controllability and  Observability    

5. Realization theory   

6. Feedback control and observer design

References: 

We will closely follow the following textbooks:

1. A Linear Systems Primer by Antsaklis and Michael, Birkhauser, 2007 (e-Book Link).   

2. Linear Systems by Antsaklis and Michael, Birkhauser, 2006 (e-Book Link).

Other reference books are the following:

1. Linear Systems Theory by Hespanha, Princeton University Press (2nd Edition), 2018.    

2. Linear System Theory and Design by Chen, Oxford University Press (4th Edition), 2013.   

3. Linear Systems by Kailath, Pearson, 2016.    

4. Linear System Theory: The State Space Approach by Zadeh and Desoer, Dover Publications, 2008. 

5. Linear Systems Theory by Rugh, Pearson (2nd Edition), 1995.

Prerequisites: Exposure to undergraduate-level linear algebra/matrix theory and differential equations is desired. We will review relevant concepts from linear algebra in the course. 

Grading policy:

Assignments: 25%

Class Participation: 5%

One Midterm: 30%,

Endterm: 40%.