Syllabus
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; Solution to LTI and LTV systems for homogeneous and non-homogeneous cases. Computation of matrix exponentials using Laplace transforms and Jordan Normal form. Applications of Eigen values and Eigen vectors.
Stability: Internal or Lyapunov stability, Lyapunov stability theorem, Eigen value conditions for Lyapunov stability, Input‐Output stability: BIBO stability, Time domain and frequency domain conditions for BIBO stabilit. BIBO versus Lyapunov stability.
Controllability and Stabilizability: Controllable and reachable subspaces, Physical examples and system interconnections, Reachability and controllability Grammians, Open loop minimum energy control, Controllability matrix(LTI), Eigen vector test for controllability, Lyapunov test for controllability, Controllable decomposition and block diagram interpretation, Stabilizable system, Eigen vector test for stabilizability, Popov‐Belevitch_Hautus (PBH) Test for stabilizability, Lyapunov test for stabilizability.
Observability and Detectability: Unobservable and unconstructable subspaces, Physical examples, observability and Constructability Grammians, Grammian based reconstruction, Duality (LTI), Observable decompositions, Kalman decomposition theorem, State estimation, Eigen value assignment by output injection, Application - Modelling, controller design and analysis of the Physical system – Analysis of implementable controllers and observers
Text Books
Same as Reference
References
1.Linear Systems Theory, Joao P. Hespanaha Princeton University Press, 2009.
2.Linear System Theory and Design, Chi‐Tsong Chen 3rd ed., Oxford, 1999.
3.Linear Systems Theory, P. Antsaklis and A. Michel McGraw Hill, 1997.
4.Linear System Theory, Wilson J. Rugh, Prentice Hall, 1996.
5.Linear System Theory and Design, Chi‐Tsong Chen, Holt, Rinehart and Winston, 1970.
6.Linear Systems, T. Kailath, Prentice Hall, 1980.
7. Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory, Dennis S. Bernstein, Princeton University Press, 2006.
Course Outcomes (COs):
CO1: Understanding basics of state-space modeling which includes representation and solution to state space
CO2: Ability to understand the physical significance of Eigenvalues and Eigenvectors
CO3: Develop skills to analyze the stability using Lyapunov stability
CO4: Can work independently to analyze the controllability and observability with applications