232-L11

Lyapunov stability routh horowitz criterion external source: https://www.tutorialspoint.com/control_systems/control_systems_stability_analysis.htm#

20 flashcards · Mathematics · by John Viljoen

  1. Define a K-class function

  2. Define locally positive definite function

  3. Define a positive definite function

  4. Define a decrescent function

  5. How do we form the first two rows of the routh array

    row one is formed from even s power coefficients of the characteristic polynomial, row two is formed from odd s power coefficients of the characteristic polynomial:

  6. how do we form the 3rd row of the routh array

  7. how do we form the 4th row of the routh array

  8. given the following characteristic polynomial what is the routh array?

  9. how do we interpret the routh array to judge stability of linear systems?

  10. what type of system is this?

    a stable focus (asymptoticaly stable)

  11. what type of system is this?

    unstable focus

  12. what can be said about this systems equilibrium points?

    every point on the x1 axis is an equilibrium point

  13. define bounded-input bounded output stability

  14. define bounded-input bounded state stability

  15. when is a continuous system unstable, even when none of its eigenvalues are in the right half plane?

  16. what function maps z to s?

  17. what function maps s to z?

  18. what are the steps to find the routh array of a discrete time system?

    find the characteristic equation in the z domain use bilinear transformation z = (1+s)/(1-s) to find the characteristic equation in the s domain form the first two rows of the routh array directly using the s domain characteristic equation use the routh array format to find subsequent rows

  19. what is a good first guess for a lyapunov function?

    the total energy of a system - its time derivative is usually tractable.

  20. what do we do if the first element of a row in the routh array is zero?

    we replace the zero with an arbritrarily small value epsilon, then when evaluating the sign changes in the routh array we take the limit as epsilon tends towards zero.