Question

From the following state-variable models, choose the expressions for the matrices A, B, C, and D for the given inputs and outputs.

The outputs are x1 and x2; the input is u.
x·1=−9x1+4x2x·1=-9x1+4x2
x·2=−3x2+8ux·2=-3x2+8u
Multiple Choice
A. A=[00], B=[08], C=[1001], and D=[−904−3]A=[00], B=[08], C=[1001], and D=[-940-3]
B. A=[00], B=[1001], C=[08], and D=[−904−3]A=[00], B=[1001], C=[08], and D=[-940-3]
C. A=[−904−3], B=[1001], C=[08], and D=[00]A=[-940-3], B=[1001], C=[08], and D=[00]
D. A=[−904−3], B=[08], C=[1001], and D=[00]

Answer 1

The accurate answer is:

A. A=[0 0; -9 4], B=[0; 8], C=[1 0; 0 -3;], and D=[-9 0; 0 -3]

Step-by-step explanation:

A matrix represents the coefficients of the state variables in the state-space equations. Based on the given state-variable models, we have x·1 = -9x1 + 4x2 and x·2 = -3x2 + 8u. Therefore, the matrix A would be [0 0; -9 4], representing the coefficients of x1 and x2 in the state equations.

B matrix represents the coefficients of the input variable (u) in the state-space equations. Based on the given state-variable models, we have x·1 = -9x1 + 4x2 and x·2 = -3x2 + 8u. Therefore, the matrix B would be [0; 8], representing the coefficient of u in the state equations.

C matrix represents the coefficients of the state variables in the output equation. Based on the given state-variable models, the outputs are x1 and x2. Therefore, the matrix C would be [1 0; 0 -3], representing the coefficients of x1 and x2 in the output equations.

D matrix represents the coefficients of the input variable (u) in the output equation. Based on the given state-variable models, the outputs are x1 and x2, and there is no direct dependence on the input u in the output equations. Therefore, the matrix D would be [0 0; 0 0], representing no direct dependence of u in the output equations.