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
