상태변수 방정식

Problem 예제.

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다음 계통의 고유값을 구하면?

[X˙1X˙2X˙3]=[010302−12−7−6][X1X2X3] \begin{bmatrix} \dot X_1\\ \dot X_2 \\ \dot X_3 \end{bmatrix} = \begin{bmatrix} 0 & 1 & 0 \\ 3 & 0 & 2 \\ -12 & -7 & -6 \end{bmatrix} \begin{bmatrix} X_1\\ X_2 \\ X_3 \end{bmatrix}

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1

λ1=−1,λ2=−2,λ3=−3 \lambda_1 = -1, \quad \lambda_2 =-2, \quad \lambda_3 = -3

2

λ1=−1,λ2=−3,λ3=−5 \lambda_1 = -1, \quad \lambda_2 =-3, \quad \lambda_3 = -5

3

λ1=0,λ2=−3,λ3=−5 \lambda_1 = 0, \quad \lambda_2 =-3, \quad \lambda_3 = -5

4

λ1=0,λ2=−2,λ3=−3 \lambda_1 = 0, \quad \lambda_2 =-2, \quad \lambda_3 = -3

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