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Quick Facts

Medium Of InstructionsMode Of LearningMode Of Delivery
EnglishSelf StudyVideo and Text Based

Course Overview

The ‘Linear Systems Theory’ online course is a study about linear systems and control associated concepts in control engineering. This course is a National Program for Technology Enhanced Learning free online program provided on the Swayam education portal. The course curriculum is developed and offered by the Indian Institute of Technology Madras.

The online program is scheduled for twelve weeks and is an elective course for undergraduate and postgraduate level students. This course which is a part of the electrical, electronics, and communication engineering along with control and instrumentation domain is a faculty development program that is approved by the All India Council for Technical Education.

The course educator for this online certification course is Prof Ramkrishna Pasumarthy from the department of electrical engineering at IIT Madras. The ‘Linear Systems Theory’ training program will allow students to gain three credits and an e-verifiable course completion certificate after completing the course.

The Highlights

  • Twelve weeks course
  • Free online training
  • Three course-credits
  • Undergraduate and postgraduate level
  • AICTE approved
  • NPTEL online program
  • E-verifiable certificate

Programme Offerings

  • Course Modules
  • videos
  • Lectures
  • Problems
  • online discussions
  • Books
  • references
  • assignments
  • Final Exam
  • E-certificate
  • Free course access
  • Three credits

Courses and Certificate Fees

Fees InformationsCertificate AvailabilityCertificate Providing Authority
INR 1000yesIIT Madras

The candidates of the ‘Linear Systems Theory’ program are provided with access to the course curriculum without any payment but are required to pay for the certification exam registration.

Linear Systems Theory fee structure

DescriptionAmount in INR
Course FeeNil
Exam FeeRs 1000

Eligibility Criteria

The students applying for the ‘Linear Systems Theory’ online program are required to have prior knowledge of linear algebra, differential equations, and control systems engineering.

Certification qualifying details

The ‘Linear Systems Theory’ e-certificate is issued to students who have a minimum average score of 10/25 (25%) in 8 out of 12 assignments, 30/75 (75%) in the exam, and a final score of 40/100 to qualify for the certification. 

What you will learn

Mathematical skillAutomation skillsKnowledge of electronicsKnowledge of engineering

The ‘Linear Systems Theory’ syllabus describes the theoretical concepts and practical applications of the aspects of linear systems and control in engineering. The students at the end of the program will be able to develop expertise in the following aspects,

  • The behavior of systems under different operating conditions
  • Linear models 
  • Control ability associated with positioning of actuators
  • Observability with regard to placing of censors
  • Design techniques such as pole placement. 
  • Fundamental of optimal control 

Who it is for

The ‘Linear Systems Theory’ online certification program is designed for the students of undergraduate or postgraduate level in electrical engineeringmechanical engineeringaerospace engineering, and chemical engineering. The course also is advantageous for the industrial professionals who are electrical engineersmechanical engineersaerospace engineers, or chemical engineers.

Admission Details

The candidates interested in applying for the ‘Linear Systems Theory’ certification program can register online through the Swayam website.

Step 1: Go to the course page using the following link,

Step 2: Click on the Sign-In/Register button

Step 3: Fill in the required information and complete the registration.

Application Details

On the registration page, the applicants will have to enter information like name, phone number, email address and others or can choose to use their valid Google or Facebook IDs to sign in.

The Syllabus

  • Introduction to Linear Systems with Examples

  • Math Preliminaries I - Vector Spaces, Bases
  • Coordinate Transformation
  • Invariant Subspaces
  • Inner product
  • Norms

  • Math Preliminaries II - Rank
  • Types of Matrices
  • Eigenvalues
  • Eigenvectors
  • Diagonalization
  • Matrix Factorization

  • State Transition Matrix
  • Solutions to LTI Systems
  • Solutions to LTV Systems

  • Equilibrium points
  • Linearization
  • Types of Linearization with Examples

  • Stability
  • Types of Stability
  • Lyapunov Equation

  • Controllability
  • Reachability
  • Stabilizability
  • Tests
  • Controllable and Reachable Subspaces
  • Grammians
  • Controllable Decomposition

  • Observability
  • Constructibility
  • Detectability
  • Tests
  • Subspaces
  • Grammians
  • State Estimation
  • Observable Decomposition

  • Kalman Decomposition
  • Pole Placement
  • Controller Design

  • Observer Design
  • Duality
  • Minimal Realization

  • Basics of Optimal Control

  • LQR, Riccati Equation

  • LMIs in Control

Evaluation process

  • The final proctored certification exam is mandatory for the students to become eligible for the course certificate.
  • The exam is conducted in the allotted centers and the registration with payment is done online through the website.
  • The minimum mark required for the certification is 30/75 (75%).


IIT Madras Frequently Asked Questions (FAQ's)

1: How long does it take to complete the ‘Linear Systems Theory’ online course?

It takes twelve weeks to complete the program.

2: What is the eligibility to attend ‘Linear Systems Theory’ classes?

The course requires the students to have background knowledge in linear algebra, differential equations, and control engineering.

3: How much is the ‘Linear Systems Theory’ training course fee?

Online training is available free for the candidates.

4: How many credits do I get at the end of the course?

The course provides three credit points.

5: How do I get my e-certificate after ‘Linear Systems Theory’ certification course completion?

You can download the e-certificate from the website.


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