How to make state space for two or more inputs with same number of state variables

I have a 2 input 4 output system of 5th order. The state space representation of the system should have 5 variables. which is obtained for single input system. But, when the state space for 2 inputs is obtained then the state variables becomes 10. and if number of inputs increases to n, the state variables also increases to 5n.

So, is there any command which can give same number of state variable with multiple inputs?

[Paul]

Can you provide some sample code that illustrates the problem? What does "obtained from a single input system" mean in the context of this question?

[Stephen23]

ankur gupta's incorrectly posted "Answer" moved here:

From input 1 to output...

0.5495 s^4 + 4.173 s^3 + 0.6189 s^2 + 0.0308 s + 0.0005129

1: ---------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

-0.0264 s^4 - 0.0021 s^3 - 0.0001041 s^2 - 1.74e-06 s - 7.999e-21

2: -----------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

-0.01548 s^4 - 0.002329 s^3 - 0.0001165 s^2 - 1.942e-06 s - 6.882e-21

3: ---------------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

-0.00131 s^4 - 0.0001983 s^3 - 9.92e-06 s^2 - 1.655e-07 s - 6.853e-22

4: ---------------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

From input 2 to output...

0.14 s^4 - 5.664 s^3 - 0.8519 s^2 - 0.0426 s - 0.0007109

1: ---------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

0.3959 s^4 + 9.834 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

2: ---------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

-0.01548 s^4 - 0.002329 s^3 - 0.0001165 s^2 - 1.942e-06 s - 6.882e-21

3: ---------------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

-0.00131 s^4 - 0.0001983 s^3 - 9.92e-06 s^2 - 1.655e-07 s - 6.853e-22

4: ---------------------------------------------------------------------

s^5 + 0.4108 s^4 + 9.836 s^3 + 1.471 s^2 + 0.07345 s + 0.001224

These are 8 equation of 2 input 4 output system. each equation can be represented by 5 state variables. How to make a combined state space for this system

Answer 1

[Paul]

Without seeing the code that constructs the model, it's unclear if the desired end state is even achievable. You can always try

doc minreal

and see where that gets you.

[Paul]

Based on the data provided, it doesn't appear that the transfer function matrix can be realized with 2 inputs, four outputs, and five states. Is there reason to believe that this should be the case based on the underlying structure of the system that is being modeled?

[Stephen23]

ankur gupta's incorrectly posted "Answer" moved here:

RSYS1=[RSYS11; RSYS21; RSYS31; RSYS41]

RSYS2=[RSYS12; RSYS22; RSYS32; RSYS42]

Two systems of 4 output and 1 input is generated from these commands. Then these two equations are combined to form a single system

RSYS=[RSYS1 RSYS2]

The direct 2x4 system can also be generated

RSYS=[RSYS11 RSYS12; RSYS21 RSYS 22; RSYS31 RSYS32; RSYS41 RSYS42]

then the state space model is obtained from command

stspc=ss(RSYS)

[Stephen23]

ankur gupta's incorrectly posted "Answer" moved here:

I have also tried append command as:

stspcRSYS1=ss(RSYS1)

stspcRSYS2=ss(RSYS2)

then these two state space are combined as:

stspc=append(stspcRSYS1,stspcRSYS2)