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IE2xx : Feedbacks and Dynamics

Linear Algebra


This course can cover modeling of dynamic (time varying) systems, with applications in business, production-inventory and socio-economic systems. Course topics include:

  • Brisk review of Introduction to Dynamical Systems and Linear Dynamical Systems (Motivation through examples in business/ industrial settings); Modeling linear dynamical systems using ODEs; Solution characterization, solution methods for first, second, higher order ODEs; Characterizing higher order ODEs as linear systems
  • Motivating examples of dynamical systems with feedback
  • Laplace transforms. Transfer functions: Block diagrams, poles, zeros, delays
  • Stability, regulation, tracking and Controllability of dynamical systems.
  • Proportional, Integral, Derivative (PID) control 
  • Root locus design method: Perspective, procedure finding root locus, design using lead, lag, notch compensation 
  • Frequency-Response Design method: Frequency-response design method, Bode/ Nyquist plots 
  • State space method: System description, block diagrams, state equations and analysis
  • Discrete systems and non-linear systems  

The second part can focus on capturing industrial and social systems using dynamics equations/ system dynamics methodology, including:

  • Stock Management Structures and Industrial Dynamics
  • Models for social systems and economics
  • Simulation of linear and non-linear systems
  • Simulation of Discrete-time and Continuous time systems


  • Chi-Tsong Chen (1998) Linear System Theory and Design, 3rd edition, Oxford University Press
  • Normal Nise, 2018,, Control Systems, Wiley India
  • Morris W. Hirsch, Robert L. Devaney and Stephen Smale (2004) Differential Equations, Dynamical Systems, and an Introduction to Chaos, 2nd edition, Academic Press.
  • John D. Sterman, 2000, Business Dynamics, McGraw Hill