# Linear Systems Theory

- Institution: IIT Madras
- Department: Electrical Engineering
- Teacher: Prof. Ramkrishna Pasumarthy
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/108106150)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/108106150)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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, design and serve as necessary foundation for further study in the area of systems and control.

Intended audience: Graduate Students from Electrical/ Mechanical/ Aerospace / Chemical Engineering

Prerequisites: 1) Linear Algebra 2) Differential Equations 3) Control Systems Engineering

## Lectures

1. [Introduction to Linear Systems](https://invisiblenetwork.ai/learn/nptel/108106150/a76688859477) (YouTube)
2. [System Models - Part 01](https://invisiblenetwork.ai/learn/nptel/108106150/444981d737b8) (YouTube)
3. [System Models - Part 02](https://invisiblenetwork.ai/learn/nptel/108106150/8f6457241bff) (YouTube)
4. [System Models - Part 03](https://invisiblenetwork.ai/learn/nptel/108106150/99a96e01511d) (YouTube)
5. [General Representation](https://invisiblenetwork.ai/learn/nptel/108106150/f8a8f036955c) (YouTube)
6. [Sets, Functions and Fields](https://invisiblenetwork.ai/learn/nptel/108106150/c1dfebc2a68c) (YouTube)
7. [Linear Algebra - Vector Spaces and Metric Spaces](https://invisiblenetwork.ai/learn/nptel/108106150/3f9d6bfa8d27) (YouTube)
8. [Linear Algebra - Span, Basis and Subspaces](https://invisiblenetwork.ai/learn/nptel/108106150/d6d0ec1d11fd) (YouTube)
9. [Linear Algebra - Linear Maps and Matrices](https://invisiblenetwork.ai/learn/nptel/108106150/68e0769a69d8) (YouTube)
10. [Linear Algebra - Fundamental Subspaces and Rank-Nullity](https://invisiblenetwork.ai/learn/nptel/108106150/715caef49004) (YouTube)
11. [Tutorial 1 on Linear Algebra](https://invisiblenetwork.ai/learn/nptel/108106150/dc7882a44d45) (YouTube)
12. [Linear Algebra - Change of Basis and Similarity Transformation](https://invisiblenetwork.ai/learn/nptel/108106150/6be70906d503) (YouTube)
13. [Linear Algebra - Invariant Subspaces, Eigen Values & Eigen Vectors](https://invisiblenetwork.ai/learn/nptel/108106150/990464dafede) (YouTube)
14. [Linear Algebra - Diagonalization and Jordan Forms](https://invisiblenetwork.ai/learn/nptel/108106150/a444cb674232) (YouTube)
15. [Linear Algebra - Eigen Decomposition and Singular Value Decomposition](https://invisiblenetwork.ai/learn/nptel/108106150/64966a774f00) (YouTube)
16. [Tutorial 2 on Linear Algebra](https://invisiblenetwork.ai/learn/nptel/108106150/87ba701a990e) (YouTube)
17. [Solutions to LTI Systems](https://invisiblenetwork.ai/learn/nptel/108106150/6b703b06781a) (YouTube)
18. [State Transition Matrix for LTI systems](https://invisiblenetwork.ai/learn/nptel/108106150/7f4fb3b0c6dd) (YouTube)
19. [Forced Reponse of Continuous and Discrete LTI system](https://invisiblenetwork.ai/learn/nptel/108106150/2699bea241ae) (YouTube)
20. [State Transition Matrix and Solutions to LTV systems](https://invisiblenetwork.ai/learn/nptel/108106150/c9277f035443) (YouTube)
21. [Equilibrium Points](https://invisiblenetwork.ai/learn/nptel/108106150/5457814bb29e) (YouTube)
22. [Limit Cycles and Linearisation](https://invisiblenetwork.ai/learn/nptel/108106150/6cb724fb756f) (YouTube)
23. [Stability Analysis & Types of Stability](https://invisiblenetwork.ai/learn/nptel/108106150/906ba22af011) (YouTube)
24. [Lyapunov Stability](https://invisiblenetwork.ai/learn/nptel/108106150/ce8615f38c5f) (YouTube)
25. [Stability of Discrete Time Systems](https://invisiblenetwork.ai/learn/nptel/108106150/cd7b3c13d229) (YouTube)
26. [Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty](https://invisiblenetwork.ai/learn/nptel/108106150/df026de87c3a) (YouTube)
27. [Controllability and Reachability](https://invisiblenetwork.ai/learn/nptel/108106150/856d21c977be) (YouTube)
28. [Controllability Matrix and Controllable Systems](https://invisiblenetwork.ai/learn/nptel/108106150/6e0b1805fa8f) (YouTube)
29. [Controllability Tests](https://invisiblenetwork.ai/learn/nptel/108106150/f1d7f9ea4dd5) (YouTube)
30. [Controllability of Discrete Time Systems](https://invisiblenetwork.ai/learn/nptel/108106150/4362cd60ddd4) (YouTube)
31. [Controllable Decomposition](https://invisiblenetwork.ai/learn/nptel/108106150/3eecd7c51839) (YouTube)
32. [Stabilizability](https://invisiblenetwork.ai/learn/nptel/108106150/724a9fe34ec4) (YouTube)
33. [Observability](https://invisiblenetwork.ai/learn/nptel/108106150/21a71c258dc0) (YouTube)
34. [Gramians and Duality](https://invisiblenetwork.ai/learn/nptel/108106150/e62234041ae2) (YouTube)
35. [Observability for Discrete Time Systems and Observability Tests](https://invisiblenetwork.ai/learn/nptel/108106150/f679f261d9cb) (YouTube)
36. [Observable Decompositon and Detectability](https://invisiblenetwork.ai/learn/nptel/108106150/33c6ea270d51) (YouTube)
37. [Kalman Decomposition and Minimal Realisation](https://invisiblenetwork.ai/learn/nptel/108106150/3c66475a1f48) (YouTube)
38. [Canonical Forms and State Feedback Control](https://invisiblenetwork.ai/learn/nptel/108106150/d4bbe1aacd28) (YouTube)
39. [Control Design using Pole Placement](https://invisiblenetwork.ai/learn/nptel/108106150/befc5559ab5b) (YouTube)
40. [Tutorial for Modules 9 and 10](https://invisiblenetwork.ai/learn/nptel/108106150/903c0c93f0a1) (YouTube)
41. [State Estimation and Output Feedback](https://invisiblenetwork.ai/learn/nptel/108106150/dd6083fd59f6) (YouTube)
42. [Design of Observer and Observer based Controller](https://invisiblenetwork.ai/learn/nptel/108106150/62397bca74a9) (YouTube)
43. [Optimal Control and Linear Quadratic Regulator (LQR)](https://invisiblenetwork.ai/learn/nptel/108106150/a633aa12ff4e) (YouTube)
44. [Feedback Invariant and Algebraic Ricatti Equation](https://invisiblenetwork.ai/learn/nptel/108106150/66a51ab939da) (YouTube)
45. [Tutorial for Module 11](https://invisiblenetwork.ai/learn/nptel/108106150/b88cd6cd82cd) (YouTube)
46. [Linear Matrix Inequalities](https://invisiblenetwork.ai/learn/nptel/108106150/1ab8115f2d66) (YouTube)
47. [Properties of LMIs and Delay LMIs](https://invisiblenetwork.ai/learn/nptel/108106150/3829e67bc00d) (YouTube)