# Linear Systems Theory

By Prof. Ramkrishna Pasumarthy   |   IIT Madras
Learners enrolled: 573
This course will provide a thorough introduction to the theory of Linear Systems with emphasis on Control related concepts. First, mathematical models describing the fundamental properties that govern the behavior of systems will be developed. We will cover time invariant, time varying, continuous and discrete time systems. This course will cover concepts of stability, controllability, observability, design and serve as necessary foundation for further study in the area of systems and control.
INTENDED AUDIENCE: Graduate Students from Electrical/ Mechanical/ Aerospace / Chemical Engineering PREREQUISITES: 1) Linear Algebra 2) Differential Equations 3) Control Systems Engineering
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Electrical, Electronics and Communications Engineering Control and Instrumentation Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 25 Jul 2022 End Date : 14 Oct 2022 Enrollment Ends : 08 Aug 2022 Exam Date : 29 Oct 2022 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Week 1: Introduction to Linear systems with Examples Week 2: Math Preliminaries I - Vector Spaces, Bases, Coordinate Transformation, Invariant Subspaces, Inner product, Norms Week 3: Math Preliminaries II - Rank, Types of Matrices, Eigen values, Eigen vectors, Diagonalization, Matrix Factorization Week 4: State Transition Matrix, Solutions to LTI Systems, Solutions to LTV Systems Week 5: Equilibrium points, Linearization, Types of Linearization with Examples Week 6: Stability, Types of Stability, Lyapunov Equation Week 7: Controllability, Reachability, Stabilizability, Tests, Controllable and Reachable Subspaces, Grammians, Controllable Decomposition Week 8: Observability, Constructibility, Detectability, Tests, Subspaces, Grammians, State Estimation, Observable Decomposition Week 9: Kalman Decomposition, Pole Placement, Controller Design Week 10: Observer Design, Duality, Minimal Realization Week 11: Basics of Optimal Control,​ ​ LQR, Ricatti Equation Week 12: LMIs in Control

### Books and references

1. Linear Algebra and its Applications​ by Gilbert Strang 2. Linear Systems Theory​ by J.H.Hespanha 3. Linear System Theory and Design ​ by C.T.Chen 4. Introduction to Dynamic Systems​ by D.G. Luenberger 5. Linear Systems ​ by P. Antsaklis and Anthony N. Michel

### Prof. Ramkrishna Pasumarthy

Ramkrishna Pasumarthy is an Associate Professor at the Dept. of Electrical Engineering, IIT Madras. He obtained his PhD in Systems and Control at the University of Twente, The Netherlands and held postdoc positions at the University of Melbourne and UCLA. He held visiting positions at Stanford University. His research interests are in the areas of network science with applications to power, traffic cloud and brain networks. also associated with the Robert Bosch Center for Data Sciences and Artificial Intelligence at IIT Madras. He also has interests in medical wearable devices and is a co funder of a start up iMov Motion Tech pvt. ltd. incubated at IITM Research Park

### 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: 29 October 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.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 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