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Linear Systems Theory

Prof. Ramkrishna Pasumarthy · IIT Madras

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About

This course will provide a thorough introduction to the theory of Linear Systems with emphasis on Control related concepts. First, mathematical models describing the fundamental properties that govern the behavior of systems will be developed. We will cover time invariant, time varying, continuous and discrete time systems. This course will cover concepts of stability, controllability, observability, design and serve as necessary foundation for further study in the area of systems and control.

Intended audience: Graduate Students from Electrical/ Mechanical/ Aerospace / Chemical Engineering

Prerequisites: 1) Linear Algebra 2) Differential Equations 3) Control Systems Engineering

Lectures

Week 1

  1. Introduction to Linear Systems YouTube
  2. System Models - Part 01 YouTube
  3. System Models - Part 02 YouTube
  4. System Models - Part 03 YouTube
  5. General Representation YouTube

Week 2

  1. Sets, Functions and Fields YouTube
  2. Linear Algebra - Vector Spaces and Metric Spaces YouTube
  3. Linear Algebra - Span, Basis and Subspaces YouTube
  4. Linear Algebra - Linear Maps and Matrices YouTube
  5. Linear Algebra - Fundamental Subspaces and Rank-Nullity YouTube
  6. Tutorial 1 on Linear Algebra YouTube

Week 3

  1. Linear Algebra - Change of Basis and Similarity Transformation YouTube
  2. Linear Algebra - Invariant Subspaces, Eigen Values & Eigen Vectors YouTube
  3. Linear Algebra - Diagonalization and Jordan Forms YouTube
  4. Linear Algebra - Eigen Decomposition and Singular Value Decomposition YouTube
  5. Tutorial 2 on Linear Algebra YouTube

Week 4

  1. Solutions to LTI Systems YouTube
  2. State Transition Matrix for LTI systems YouTube
  3. Forced Reponse of Continuous and Discrete LTI system YouTube
  4. State Transition Matrix and Solutions to LTV systems YouTube

Week 5

  1. Equilibrium Points YouTube
  2. Limit Cycles and Linearisation YouTube

Week 6

  1. Stability Analysis & Types of Stability YouTube
  2. Lyapunov Stability YouTube
  3. Stability of Discrete Time Systems YouTube
  4. Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty YouTube

Week 7

  1. Controllability and Reachability YouTube
  2. Controllability Matrix and Controllable Systems YouTube
  3. Controllability Tests YouTube
  4. Controllability of Discrete Time Systems YouTube
  5. Controllable Decomposition YouTube
  6. Stabilizability YouTube

Week 8

  1. Observability YouTube
  2. Gramians and Duality YouTube
  3. Observability for Discrete Time Systems and Observability Tests YouTube
  4. Observable Decompositon and Detectability YouTube

Week 9

  1. Kalman Decomposition and Minimal Realisation YouTube
  2. Canonical Forms and State Feedback Control YouTube
  3. Control Design using Pole Placement YouTube
  4. Tutorial for Modules 9 and 10 YouTube

Week 10

  1. State Estimation and Output Feedback YouTube
  2. Design of Observer and Observer based Controller YouTube

Week 11

  1. Optimal Control and Linear Quadratic Regulator (LQR) YouTube
  2. Feedback Invariant and Algebraic Ricatti Equation YouTube
  3. Tutorial for Module 11 YouTube

Week 12

  1. Linear Matrix Inequalities YouTube
  2. Properties of LMIs and Delay LMIs YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Electrical Engineering
Teacher
Prof. Ramkrishna Pasumarthy
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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