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  • 7:20 PM, Monday, 18 Oct 2021

Course Postgraduate
Semester Sem. I
Subject Code AVC612
Subject Title Linear Control System


Introduction to Modern Control Theory : Introduction to state‐space versus transform methods in linear systems; internal versus input/output formulation; discrete‐time and continuous‐ time systems;. Fundamental concepts of linearity, causality, time‐invariance, Solution to LTI and LTV systems, Solutions to homogeneous and non homogeneous cases. Computation of matrix exponentials using Laplace transforms and Jordan Normal form, positive definite matrices, quadratic forms

Stability: Internal or Lyapunov stability, Lyapunov stability theorem, Eigen value conditions for Lyapunov stability, Continuous and Discrete time cases, Input‐Output stability: BIBO stability,Time domain conditions for BIBO stability. Frequency domain conditions for BIBO stability. BIBO versus Lyapunov stability.

Controllability and Stabilizability: Controllable and reachable subspaces, Physical examples and system interconnections, Reachabilty and controllability Grammians, Open loop minimum energy control, Controllabilty matrix(LTI), Eigen vector test for controllability, Lyapunov test for controllability, Controllable decomposition and block diagram interpretation, Stabilizable system, Eigen vector test for stabilizabilty, Popov‐Belevitch_Hautus (PBH) Test for stabilizabilty, Lyapunov test for stabilizabilty. Feedback stabilization based on Lyapunov test.

Observabilty and Detectability: Unobservable and unconstructable subspaces, Physical examples, observabilty and Constructabilty Grammians, Gramian based reconstruction, Duality(LTI), Observable decompositions, Kalman decomposition theorem, Detectability, detectability tests, State estimation, Eigen value assignment by output injection, Stabilization through output feedback.

Text Books
  1. Joao P. Hespanaha, Linear Systems Theory. Princeton University Press, 2009.
  2. Chi‐Tsong Chen, Linear System Theory and Design, 3rd ed., Oxford,1999.
  3. P. Antsaklis and A. Michel, Linear Systems Theory, McGraw Hill, 1997.
  4. Wilson J. Rugh, Linear System Theory, Prentice Hall, 1996.
  5. Chi‐Tsong Chen, Linear System Theory and Design, Holt, Rinehart and Winston, 1970.
  6. T. Kailath, Linear Systems, Prentice Hall, 1980.
  7. F.M. Callier and C.A. Desoer, Linear System Theory, Springer‐ Verlag, 1991.
  8. W. S. Levine,, The Control Handbook, CRC press, 1996.
  9. W. M Wonham, Linear multivariable control ‐ A geometric approach, New York, Springer‐ Verlag New York, Inc. (Applications of Mathematics. Volume 10), 1979.

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