Course Details
Subject {L-T-P / C} : EE6301 : Linear System Theory { 3-0-0 / 3}
Subject Nature : Theory
Coordinator : Prof. Asim Kumar Naskar
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
- 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 <br />CO1. Understand the concept of solution, independent solution and solvability of ordinary differential equations. <br />CO2. Represent different dynamical systems in linear state space form. <br />CO3. Solve autonomous and non-autonomous linear dynamical systems. <br />CO4. Realize SISO and MIMO transfer functions. <br />CO5. Use the concepts of controllability, observability, invariant subspace, and control-invariant subspaces. <br />CO6. Design different state feedback control laws for SISO and MIMO systems. <br />CO7. Design the full order and reduced order observer.
Essential Reading
- S.H. Zak, Systems and Control, Oxford Univ. Press
- J.S.Bay, Fundamental of Linear State Space Systems, MacGraw-Hill
Supplementary Reading
- M. Gopal, Digital Control and State Variable Methods, Tata McGraw-Hill
- B. Friedland, Control System Design - An Introduction to State-Space Methods, MacGraw-Hill