Lecture 1 - Introduction to Linear Systems

Lecture 2 - System Models

Lecture 3 - System Models - Part 1

Lecture 4 - System Models - Part 2

Lecture 5 - General Representation

Lecture 6 - Sets, Functions and Fields

Lecture 7 - Linear Algebra - Vector Spaces and Metric Spaces

Lecture 8 - Linear Algebra - Span, Basis and Subspaces

Lecture 9 - Linear Algebra - Linear Maps and Matrices

Lecture 10 - Linear Algebra - Fundamental Subspaces and Rank-Nullity

Lecture 11 - Tutorial 1 on Linear Algebra

Lecture 12 - Linear Algebra - Change of Basis and Similarity Transformation

Lecture 13 - Linear Algebra - Invariant Subspaces, Eigen Values and Eigen Vectors

Lecture 14 - Linear Algebra - Diagonalization and Jordan Forms

Lecture 15 - Linear Algebra - Eigen Decomposition and Singular Value Decomposition

Lecture 16 - Tutorial 2 on Linear Algebra

Lecture 17 - Solutions to LTI Systems

Lecture 18 - State Transition Matrix for LTI systems

Lecture 19 - Forced Reponse of Continuous and Discrete LTI system

Lecture 20 - State Transition Matrix and Solutions to LTV systems

Lecture 21 - Equilibrium Points

Lecture 22 - Limit Cycles and Linearisation

Lecture 23 - Stability Analysis and Types of Stability

Lecture 24 - Lyapunov Stability

Lecture 25 - Stability of Discrete Time Systems

Lecture 26 - Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty

Lecture 27 - Controllability and Reachability

Lecture 28 - Controllability Matrix and Controllable Systems

Lecture 29 - Controllability Tests

Lecture 30 - Controllability of Discrete Time Systems

Lecture 31 - Controllable Decomposition

Lecture 32 - Stabilizability

Lecture 33 - Observability

Lecture 34 - Gramians and Duality

Lecture 35 - Observability for Discrete Time Systems and Observability Tests

Lecture 36 - Observable Decompositon and Detectability

Lecture 37 - Kalman Decomposition and Minimal Realisation

Lecture 38 - Canonical Forms and State Feedback Control

Lecture 39 - Control Design using Pole Placement

Lecture 40 - Tutorial for Modules 9 and 10

Lecture 41 - State Estimation and Output Feedback

Lecture 42 - Design of Observer and Observer based Controller

Lecture 43 - Optimal Control and Linear Quadratic Regulator (LQR)

Lecture 44 - Feedback Invariant and Algebraic Ricatti Equation

Lecture 45 - Tutorial for Module 11

Lecture 46 - Linear Matrix Inequalities

Lecture 47 - Properties of LMIs and Delay LMIs