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Lyapunov Stability
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Classroom Contents
Linear System Theory
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- 1 System Models - Part 01
- 2 Linear Algebra - Span, Basis and Subspaces
- 3 Introduction to Linear Systems
- 4 System Models - Part 02
- 5 System Models - Part 03
- 6 General Representation
- 7 Sets, Functions and Fields
- 8 Linear Algebra - Vector Spaces and Metric Spaces
- 9 Linear Algebra - Linear Maps and Matrices
- 10 Tutorial 1 on Linear Algebra
- 11 Linear Algebra - Diagonalization and Jordan Forms
- 12 Linear Algebra - Eigen Decomposition and Singular Value Decomposition
- 13 Tutorial 2 on Linear Algebra
- 14 Linear Algebra - Change of Basis and Similarity Transformation
- 15 Linear Algebra - Invariant Subspaces, Eigen Values & Eigen Vectors
- 16 Linear Algebra - Fundamental Subspaces and Rank-Nullity
- 17 Solutions to LTI Systems
- 18 State Transition Matrix for LTI systems
- 19 Forced Reponse of Continuous and Discrete LTI system
- 20 State Transition Matrix and Solutions to LTV systems
- 21 mod05lec21-Equilibrium Points
- 22 mod05lec22-Limit Cycles and Linearization
- 23 Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty
- 24 Stability of Discrete Time Systems
- 25 Lyapunov Stability
- 26 Stability Analysis & Types of Stability
- 27 Stabilizability
- 28 Controllable Decomposition
- 29 Controllability of Discrete Time Systems
- 30 Controllability Tests
- 31 Controllability Matrix and Controllable Systems
- 32 Controllability and Reachability
- 33 Observability for Discrete Time Systems and Observability Tests
- 34 Gramians and Duality
- 35 Observability
- 36 Observable Decompositon and Detectability
- 37 Tutorial for Modules 9 and 10
- 38 Control Design using Pole Placement
- 39 Canonical Forms and State Feedback Control
- 40 Kalman Decomposition and Minimal Realisation
- 41 mod10lec42-Design of Observer and Observer based Controller
- 42 mod10lec41-State Estimation and Output Feedback
- 43 mod11lec45-Tutorial for Module 11
- 44 mod11lec44-Feedback Invariant and Algebraic Ricatti Equation
- 45 mod11lec43-Optimal Control and Linear Quadratic Regulator (LQR)
- 46 mod12lec46-Linear Matrix Inequalities
- 47 mod12lec47-Properties of LMIs and Delay LMIs
