Course Details

Subject {L-T-P / C} : EE6301 : Linear System Theory {3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Susovon Samanta

Syllabus

Review of Linear algebra: Vectors and Vector Spaces, Linear Combinations and Bases, eigenvalue and eigenvectors. State Space Analysis: State-space approach to linear system theory, State space representation of different dynamical system, representing transfer function in different canonical forms such as controllable and observable canonical forms, Jordan form, solutions of state equations using different methods (time invariant and time varying systems) System Analysis: Controllability, Observability, Kalman decomposition, Stabilizability and Detectability, Duality State Feedback Design: State variable feedback, pole placement for single and multivariable systems, state feedback with integral control, asymptotic tracking and regulation, optimal control concept, solution of linear quadratic regulator State Estimation: State observer, reduced order observers, combined observer-controller system, Stability: Basic concepts, Stability theorem, Lyapunov functions for LTI systems.

Course Objectives

  1. For the students to become familiar with some modern control theories and techniques, such as state space representation of the different dynamical systems, solution of the state equation, state transition matrix, controllability and observability, pole placement design, state observer and Lyapunov stability analysis.

Course Outcomes

At the end of the course students will be able to
• Represent different dynamical systems in state space form
• Solve the state space dynamical systems to get the transient response with different inputs.
• Check the system two important properties such as controllability and observability.
• Design the state feedback control law for regulation as well as for tracking problem.
• Design the full order and reduced order observer
• Check the stability of the dynamical systems using Lyapunov method

Essential Reading

  1. S.H. Zak, Systems and Control, Oxford Univ. Press
  2. J.S.Bay, Fundamental of Linear State Space Systems, MacGraw-Hill

Supplementary Reading

  1. M. Gopal, Digital Control and State Variable Methods, Tata McGraw-Hill
  2. B. Friedland, Control System Design - An Introduction to State-Space Methods, MacGraw-Hill