Linear System Theory

Linear System Theory

@VTU COE

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What you will learn

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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.

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Sets, Functions and Fields
Preview 24:26
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Linear Algebra - Vector Spaces and Metric Spaces
Preview 23:50
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Linear Algebra - Span, Basis and Subspaces
Preview 34:30
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Linear Algebra - Linear Maps and Matrices
Preview 18:28
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Linear Algebra - Fundamental Subspaces and Rank-Nullity
Preview 48:04
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Tutorial 1 on Linear Algebra
Preview 31:13

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Linear Algebra - Change of Basis and Similarity Transformation
Preview 31:42
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Linear Algebra - Invariant Subspaces, Eigen Values & Eigen Vectors
Preview 46:39
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Linear Algebra - Diagonalization and Jordan Forms
Preview 43:46
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Linear Algebra - Eigen Decomposition and Singular Value Decomposition
Preview 19:06
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Tutorial 2 on Linear Algebra
Preview 28:17

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Solutions to LTI Systems
Preview 20:23
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State Transition Matrix for LTI systems
Preview 26:06
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Forced Reponse of Continuous and Discrete LTI system
Preview 20:24
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State Transition Matrix and Solutions to LTV systems
Preview 33:37

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Equilibrium Points
Preview 49:24
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Limit Cycles and Linearisation
Preview 34:34

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Stability Analysis & Types of Stability
Preview 28:35
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Lyapunov Stability
Preview 64:10
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Stability of Discrete Time Systems
Preview 20:27
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Supplementary Lecture: Comparison Lemma and Lyapunov Stabilty
Preview 28:26

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Controllability and Reachability
Preview 50:40
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Controllability Matrix and Controllable Systems
Preview 28:51
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Controllability Tests
Preview 52:32
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Controllability of Discrete Time Systems
Preview 40:44
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Controllable Decomposition
Preview 16:48
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Stabilizability
Preview 53:42

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Observability
Preview 19:52
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Gramians and Duality
Preview 27:18
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Observability for Discrete Time Systems and Observability Tests
Preview 16:48
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Observable Decompositon and Detectability
Preview 15:54

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Kalman Decomposition and Minimal Realisation
Preview 52:51
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Canonical Forms and State Feedback Control
Preview 17:19
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Control Design using Pole Placement
Preview 38:13
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Tutorial for Modules 9 and 10
Preview 23:44

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State Estimation and Output Feedback
Preview 34:42
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Design of Observer and Observer based Controller
Preview 40:31

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Optimal Control and Linear Quadratic Regulator (LQR)
Preview 49:33
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Feedback Invariant and Algebraic Ricatti Equation
Preview 54:11
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Tutorial for Module 11
Preview 28:52

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Linear Matrix Inequalities
Preview 30:59
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Properties of LMIs and Delay LMIs
Preview 53:46
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Meet Your Instructor
@VTU COE
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Instructor
3.2 Rating
2542 Students
759 Courses
About Instructor

VTU is one of the largest Technological Universities in India with 24 years of Tradition of excellence in Engineering & Technical Education, Research and Innovations. It came into existence in the year 1998 to cater the needs of Indian industries for trained technical manpower with practical experience and sound theoretical knowledge.

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Free

  • Course Duration
    25 h 53 m 17 s
  • Course Level
    Intermediate
  • Student Enrolled
    0
  • Language
    English
This Course Includes
  • 25 h 53 m 17 s Video Lectures
  • 0 Quizzes
  • 0 Assignments
  • 0 Downloadable Resources
  • Full Lifetime Access
  • Certificate of Completion