NOC:Linear System Theory


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