Question

8. Consider the following system represented in state space: \( \dot{x} = Ax + Bu \) Where \( A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -6 & -k & -3 \end{bmatrix} \) and \( B = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \) (a) Determine the characteristic equation of the above system. (b) Find the range of \( k \) where this system is stable. Hint: Use Routh-Hurwitz method for (b).

          8. Consider the following system represented in state space:
\( \dot{x} = Ax + Bu \)
Where \( A = \begin{bmatrix} 0 & 1 & 0 \\ 0 & 0 & 1 \\ -6 & -k & -3 \end{bmatrix} \) and \( B = \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix} \)
(a) Determine the characteristic equation of the above system.
(b) Find the range of \( k \) where this system is stable.
Hint: Use Routh-Hurwitz method for (b).

8. Consider the following system represented in state space:
ẋ = Ax + Bu
Where A =
< b m a t r i x > and B =
< b m a t r i x >
(a) Determine the characteristic equation of the above system.
(b) Find the range of k where this system is stable.
Hint: Use Routh-Hurwitz method for (b).

Added by Stacy R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

08/16/2023

Step 1

For the given system: A = [[0, 1, 0], [0, 0, -6], [1, 0, -k]] The characteristic equation is det(sI - A) = det([[s, -1, 0], [0, s, 6], [-1, 0, s+k]]) = Show more…

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Consider the following system represented in state space: x_()=^(˙)Ax_(+)Bu Where A=[[0,1,0,0,1,-k,-3]] -6 0 and B=[[0]] 0 1 (a) Determine the characteristic equation of the above system. (b) Find the range of k where this system is stable. Hint: Use Routh-Hurwitz method for (b). 8. Consider the following system represented in state space: x = Ax + Bu 0 0 -6 1 0 -k 0 0 1 and B= 0 3] Where A= (a Determine the characteristic equation of the above system (b) Find the range of k where this system is stable. Hint: Use Routh-Hurwitz method for (b)