National Instruments 370753C-01 Manual De Usuario

X0

0

Input Names

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Input 1 

Output Names

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Output 1

System is continuous

T (a square matrix) =

2.22045e-16 0 

-1 

0 1 

0 

-1 0 

2.22045e-16

nuc (a scalar) = 2

These results indicate that only the first state of the system corresponds to 
a controllable mode, and the remaining two are uncontrollable.

Similarly, if you form the controllability matrix for this system,

[,states] = size(A);

Con = B;

For i = 1:states-1;

Con = [B, A*Con];

endFor

det(Con)

ans (a scalar) = 0

you see that the controllability matrix is singular (its determinant is zero), 
confirming the results from 

controllable( )

. 

As described in the 

 section, the term controllability 

describes whether or not a system’s states can be affected, and the system 
eigenvalues relocated, by changes to the system input. The analogous 
concept of observability describes whether it is possible to determine the 
value of an individual state at a particular time by observing the system 
outputs for a finite amount of time. In essence, an observable system is one 
for which you can “observe” state values by knowing the output of the 
system.