E1 241: Dynamics of Linear Systems


Vaibhav Katewa
Assistant Professor
Department of Electrical Communication Engineering (ECE) / Robert Bosch Center for Cyber-Physical Systems (RBCCPS)
Email: vkatewa(at)iisc(dot)ac(dot)in

Class Timings

Tue-Thu, 2:00-3:30 PM. First class is on Aug. 05, 2021.


Online on Microsoft Teams. The link to join the class lectures is here.

The link to join the Teams group is here.

Class Logistics

We will have live lectures on Microsoft Teams. These lectures will be recorded and made available to the students after each class along with the handwritten notes. The registered students will be added to a Class group in Microsoft Teams. Thereafter, all the course correspondence will happen in this Teams group.

Teaching Assistants

  1. Varkey M John (Email:varkeym(at)iisc(dot)ac(dot)in)

  2. Nishchal Hoysal G (Email:nishchalg(at)iisc(dot)ac(dot)in)

Course Overview and 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 mathematical analysis of these system 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


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


  1. Homeworks: 30%

  2. One Midterm: 30%

  3. Endterm: 40%


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)

The second book is a more comprehensive treatment of the first one. Both the books are available for download using IISc institutional access. You may have to connect via VPN to access the links. Other reference books are:

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

  4. Linear Systems by Kailath, Pearson, 2016.

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