User`s guide

ctrb
11-43
11ctrb
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
(11-1)
where has n rows and nm columns.
Co = ctrb(sys) calculates the controllability matrix of the state-space LTI
object
sys.Thissyntaxisequivalenttoexecuting
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