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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
Description:
COURSE OUTLINE: 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, and design and serve as a necessary foundation for further study in the area of systems and control.

Linear System Theory

NPTEL
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#Engineering #Electrical Engineering #Mathematics #Algebra #Linear Algebra #Control Systems #Stability Analysis #Singular Value Decomposition
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System Models - Part 01