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# Advanced Linear Continuous Control Systems

IIT Roorkee, , Prof. Prof. Yogesh Vijay Hote

Updated On 02 Feb, 19

##### Overview

Today, there is an utmost need to understand advanced control engineering on account of its multidisplinary applications in various areas of engineering. The main thrust in this course is on fundamentals of advanced linear continuous control system. In this course, various methodology of modelling in state space, state transition matrix and solution in state equation will be studied. Further, stability analysis issues in state space will be discussed. Finally, the concepts of controllability, observability, controller design, and observer design will also be discussed. The theory is supported by numerical examples, practical examples and Matlab programming

## Lecture 18: Stability Analysis in State Space: Lyapunov Stability Analysis (Sylvester’s Criterion) Part-III

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### COURSE LAYOUT

Week 1  :1   Introduction to State Space
2   State Space Representation
3   State Space Representation: Companion Form (Controllable Canonical Form)
4   State Space Representation :Extended Controllable Canonical Form
5   State Space Representation :Observable Canonical Form
Week 2  : 1   State Space Representation: Diagonal Canonical Form (Part I)
2   State Space Representation: Diagonal Canonical Form (Part II)
3   State Space Representation: Jordan Canonical Form
4   State Space Representation: Numerical Examples on State Space Modelling (Part I)
5   State Space Representation: Numerical Examples on State Space Modelling (Part II)
Week 3 :  1   Modelling of Mechanical Systems in State Space
2   Modelling of DC Servo Motor (Part I)
3   Modelling of DC Servo Motor (Part II)
4   Determination of Transfer Function from State Space Model (Part-I)
5   Determination of Transfer Function from State Space Model (Part-II)
Week 4  : 1    Stability Analysis in State Space:Concept of Eigenvalues and Eigenvectors (Part I)
2    Stability Analysis in State Space (Part II)
3    Stability Analysis in State Space:Lyapunov Stability Analysis (Sylvesters Criterion) (Part III)
4    Stability Analysis in State Space:Lyapunov Stability Analysis (Stability Criterion) (Part IV)
5    Stability Analysis in State Space:Lyapunov Stability Analysis (Direct Method) (Part V)
Week 5  : 1    Concept of Diagonalization
2    Solution of State Equation
3    Solution of State Equation (Forced system)
4    Steady State Error for State Space System
5    State Transition Matrix (Part-I)
Week 6  :  1    State Transition Matrix (Part-II)
2    State Transition Matrix using Caley Hamilton Theorem (Part-III)
3    MATLAB Programming with State Space
4    Controllability in State Space (Part-I)
5    Controllability in State Space (Part-II)
Week 7  :  1   Observability in State Space (Part-I)
2    Observability in State Space (Part-II)
3    Pole Placement by State Feedback (Part-I)
4    Pole Placement by State Feedback (Part-II)
5    Pole Placement by State Feedback (Part-III)
Week 8  :  1    Tracking Problem in State Feedback Design (Part-I)
2    Tracking Problem in State Feedback Design (Part-II)
3    State Observer Design (Part-I)
4    State Observer Design (Part-II)
5    State Observer Design (Part-III)

Thanks to the support from MathWorks, enrolled students have access to MATLAB for the duration of the course.

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###### Comments

Sam

Excellent course helped me understand topic that i couldn't while attendinfg my college.

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Dembe

Great course. Thank you very much.

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