# How does state space form include input delay in MATLAB?

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Sol Elec on 9 Apr 2022
Edited: Sam Chak on 10 Apr 2022
I got this code from 'Time Delays in Linear System' MATLAB help.
A=-2; B=3; C=[1;-1];D=0;
G = ss(A,B,C,D,'InputDelay',1.5)
Now I want to implement this in another model where matrix are-
A=[1 2 3;4 3 2;1 2 3]; C=[0 3 0];
D=[0 -1];
B=[3;5;7];
H = ss(A,B,C,D,'InputDelay',[1.5;2.1;3.2])
But after running the above code, we got an error. "The values of the "a" and "b" properties must be matrices with the same number of rows.".
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Sol Elec on 9 Apr 2022
@Star Strider After correcting D=[-1]; again get this error-Error using ss (line 345)
The value of the "InputDelay" property must be a vector with as many entries as input channels.
Star Strider on 10 Apr 2022
Exactly.
And ‘B’ and ‘D’ are not the same sizes, an additional error.

Sam Chak on 9 Apr 2022
Edited: Sam Chak on 9 Apr 2022
If you look at the matrices for the desired state-space system
A =
1 2 3
4 3 2
1 2 3
B =
3
5
7
C =
0 3 0
D =
0 -1
you'll see that the system matrices C(1x3), B(3x1) and D(1x2) are definitely incompatible.
The dimension of D should be (1x1) because the dimension of is .
Another possibility is that if the dimension of D is (1x2), then it implies there are two inputs and the dimension of B must be (3x2).
In general, it should satisfy this:
when you type this out:
[A B; C D]
Sol Elec on 9 Apr 2022
Edited: Sol Elec on 9 Apr 2022
@Sam Chak After modifying D=[-1];
I got this error- Error using ss (line 345)
The value of the "InputDelay" property must be a vector with as many entries as input channels.
Sam Chak on 10 Apr 2022
Edited: Sam Chak on 10 Apr 2022
The error stemmed from a set of 3 tau's for a single input, u1:
'InputDelay', [1.5; 2.1; 3.2]
If there is only 1 tau in the input u1, then your state-space model looks like this:
A = [1 2 3; 4 3 2; 1 2 3];
B = [3; 5; 7];
C = [0 3 0];
D = [-1];
sys = ss(A, B, C, D, 'InputDelay', 1.5)
sys =
A =
x1 x2 x3
x1 1 2 3
x2 4 3 2
x3 1 2 3
B =
u1
x1 3
x2 5
x3 7
C =
x1 x2 x3
y1 0 3 0
D =
u1
y1 -1
Input delays (seconds): 1.5
Continuous-time state-space model.
In transfer function form of the time-delayed SISO system looks like this:
[num, den] = ss2tf(A, B, C, D);
G = tf(num, den, 'InputDelay', 1.5)
G =
-s^3 + 22 s^2 + 18 s + 120
exp(-1.5*s) * ------------------------------------
s^3 - 7 s^2 - 7.47e-15 s + 4.174e-15
Continuous-time transfer function.
If you confirm that there are 3 inputs with time delays, then the sample code is given by:
A = [1 2 3; 4 3 2; 1 2 3];
B = eye(3);
C = [0 3 0];
D = [0 0 0];
sys = ss(A, B, C, D, 'InputDelay', [1.5; 2.1; 3.2])
sys =
A =
x1 x2 x3
x1 1 2 3
x2 4 3 2
x3 1 2 3
B =
u1 u2 u3
x1 1 0 0
x2 0 1 0
x3 0 0 1
C =
x1 x2 x3
y1 0 3 0
D =
u1 u2 u3
y1 0 0 0
Input delays (seconds): 1.5 2.1 3.2
Continuous-time state-space model.
Hope this clears up your confusion.