Module 9 : Robot Dynamics & controls
Lecture 34 : Trajectory tracking control ( feed forward, computed torque and inverse dynamics approach)
Quadratic Functions :
Very popular function used in Lyapunov theory applied to robots.
  Quadratic functions can be written in the form
 
  in matrix form where
  & X is a state vecor.
  Theorem:
1.

Quadratic functions are positive definite functions if determinants of successive minors of A are all positive.

  e.g , & so on should be positive.
2.
Quadratic functions are positive definite functions if eigenvalues of A are all positive. eigen(A) >0, i=1,2,...n
 
Contd...
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