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LME Reference — linear algebra
331
With two or three output arguments, (X,L,K) = care(...) also returns the gain matrix K defined as
K = R−1 B0 X
and the column vector of closed-loop eigenvalues
L = eig(A − BK)
care(A,S,Q,true) with up to two output arguments is equivalent to
care(A,B,Q) or care(A,B,Q,false) with S=B*B’.
Example
A =
B =
C =
Q =
R =
(X,
X
[-4,2;1,2];
[0;1];
[2,-1];
C’ * C;
5;
L, K) = care(A, B, Q, R)
=
1.07
3.5169
3.5169
23.2415
L =
-4.3488
-2.2995
K =
0.7034
4.6483
A’ * X + X * A - X * B / R * B’ * X + Q
1.7319e-14 1.1369e-13
8.5265e-14 6.2528e-13
See also
dare
chol
Cholesky decomposition.
Syntax
M2 = chol(M1)
Description
If a square matrix M1 is symmetric (or hermitian) and positive definite,
it can be decomposed into the following product:
M1 = M02 M2