Courses » Dynamical Systems and Control

Dynamical Systems and Control


This course ‘Dynamical systems and control’ is a basic course offered to PG students and final year UG students of Engineering/Science background. The objective of this course is to enhance the understanding of the theory, properties and applications of various dynamical and control systems. After completing the course one may be able to understand some of the important aspects of dynamical systems such as mathematical modeling, well posedness (existence, uniqueness and stability) of the considered problem. The participants will also be conversant with the controllability, stabilizability and optimal control aspects of a dynamical system.
 Most Dynamical systems-physical, social, biological, engineering are often conveniently expressed (modeled) in the form of differential equations with or without control. Such mathematical models can provide an insight into the behavior of real life system if appropriate mathematical theory and techniques are applied. In this context this course has tremendous applications in diverse fields of engineering and technology.

UG/PG students of technical institutions/ universities/colleges.

CORE/ELECTIVE: Core and Elective


PREREQUISITES: Basic concepts from Linear Algebra and Ordinary Differential Equations


499 students have enrolled already!!


Dr. N. Sukavanam is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes Control Theory and Robotics. He has supervised nineteen Ph.D. thesis and has published more than 80 research papers in reputed international journals. He coordinated five QIP short term courses and a Continuing Education course on Dynamical Systems, Control Theory and Robotics and has delivered many invited lectures on these subjects in many institutions of national importance. He has developed the online course on Mathematics-1 under the Pedagogy project(Main Phase) jointly with Dr. P. Bera, Department of Mathematics, IIT Roorke. He has taught various courses on Dynamical Systems and Control Theory for B. Tech./M. Sc./Ph. D classes several times in the last 20 years.

Dr. D. N. Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. Before joining IIT Roorkee, he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. His area of expertise includes semigroup theory and functional differential equations of fractional and integral orders. He has already prepared e-notes for the course titled “Ordinary Differential Equations and Special Functions” under e-Pathshala funded by UGC. Also, he has published a book titled “Nonlocal Functional Evolution Equations: Integral and fractional orders, LAP LAMBERT Academic Publishing AG Germany”. He has delivered several invited talks at reputed institutions in India and abroad. He has guided three PhD theses and has published more than 60 papers in various international journals of repute. Currently, he is supervising five research students.


Week 1  :  Formulation of physical systems-I, Formulation of physical systems-II, Existence and uniqueness theorems-I, Existence and uniqueness theorems-II, Linear systems-I
Week 2  :   Linear Systems-II, Solution of linear systems-I, Solution of linear systems–II, Solution of linear systems-III, Fundamental Matrix-I
Week 3 :  Fundamental Matrix-II, Fundamental matrices for non- autonomous systems, Solution of non-homogeneous systems , Stability of systems: Equilibrium points, Stability of linear autonomous systems-I
Week 4  :  Stability of linear autonomous systems-II, Stability of linear autonomous systems-III, Stability of weakly non-  linear systems-I, Stability of weakly non-  linear systems-II, Stability of non-  linear systems using linearization
Week 5  :   Properties  of phase portrait, Properties  of orbits, Phase portrait : Types of critical points, Phase portrait of linear differential equations-I, Phase portrait of linear differential equations-II
Week 6  :   Phase portrait of linear differential equations-III, Poincare Bendixson Theorem, Limit cycle , Lyapunov stability-I, Lyapunov stability–II
Week 7 :   Introduction to Control Systems-I, Introduction to Control Systems-II, Controllability of Autonomous Systems, Controllability of Non-autonomous Systems, Observability-I
Week 8  :  Observability-II,  Results on Controllability and Observability,  Companion Form,  Feedback Control-I, Feedback Control-II
Week 9  :   Feedback Control-III, Feedback Control-IV,  State Observer, Stabilizability, Introduction to Discrete Systems-I
Week 10  :  Introduction to Discrete Systems-II,  Lyapunov Stability Theory-I,  Lyapunov Stability Theory-II,  Lyapunov Stability Theory-III, Optimal Control- I
Week 11  :   Optimal Control-II, Optimal Control-III, Optimal Control- IV, Optimal Control for Discrete Systems-I,  Optimal Control for Discrete Systems-II
Week 12  :  Controllability of Discrete Systems, Observability of Discrete Systems, Stability for Discrete Systems, Relation between Continuous and Discrete Systems-I,  Relation between Continuous and Discrete Systems-II


Braun, M. “Differential Equations and Their Applications”, 4th Ed., Springer 2011.2. Stephen Barnett, Introduction to Mathematical Control Theory, Oxford University Press, 1990 3. D. Subbaram Naidu, Optimal Control Systems, CRC Press, 20034. Deo, S.G., Lakshmikantham, V., and Raghvendra, V.,"Text Book of Ordinary Differential Equations”, 2nd Ed., Tata McGraw Hill 2010.5. M. Gopal, Modern Control System Theory, John Wiley & Sons Ltd., 1994. 6. . Simmons G.F., “Ordinary Differential Equations with Applications”, Tata McGraw Hill 2003.
  • The exam is optional for a fee.
  • Date and Time of Exams: April 28 2019(Sunday)  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.


  • Final score will be calculated as : 25% assignment score + 75% final exam score
  • 25% assignment score is calculated as 25% of average of  Best 8 out of 12 assignments
  • E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. 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 Roorkee.It will be e-verifiable at nptel.ac.in/noc.