Specifications

ctrb
16-45
16ctrb
Purpose Form the controllability matrix
Syntax Co = ctrb(A,B)
Co = ctrb(sys)
Description ctrb computes the controllability matrix for state-space systems. For an
n-by-n matrix
A and an n-by-m matrix B, ctrb(A,B) returns the controllability
matrix
(16-1)
where has n rows and nm columns.
Co = ctrb(sys) calculates the controllability matrix of the state-space LTI
object
sys. This syntax is equivalent to executing
Co = ctrb(sys.A,sys.B)
The system is controllable if Co has full rank n.
Example Check if the system with the following data
A =
1 1
4 -2
B =
1 -1
1 -1
is controllable. Type
Co=ctrb(A,B);
% Number of uncontrollable states
unco=length(A)-rank(Co)
and MATLAB returns
unco =
1
Co
BABA
2
B
…
A
n 1–
B
=
Co