care

Solves the continuous-time Algebraic Riccati Equation.

Syntax

[X, L, G] = care(A, B, Q)

[X, L, G] = care(A, B, Q, R)

[X, L, G] = care(A, B, Q, R, S, E)

Inputs

A
The state matrix (n x n), where n is the number of states.
B
The control matrix (n x p), where p is the number of inputs.
Q
The state cost matrix (n x n).
R
The control cost matrix (p x p).
S
Optional real matrix (n x p).
E
The descriptor matrix (n x n).

Outputs

X
The unique stabilized solution of the Riccati equation (n x n) in continuous time.
1
The closed-loop pole vector (n x 1).
g
The gain matrix (p x n).

Example

Include the care function: 
 A = [-15 1; 0.5 5];
B = [0; 5];
Q = [5, -0.5];
r = 1.5;
[X, L, G] = care(A, B, Q'*Q, r)
X = [Matrix] 2 x 2
 0.82854  -0.06766
-0.06766   0.61126
L = [Matrix] 2 x 1
-15.16316
-5.02446
G = [Matrix] 1 x 2
-0.22552  2.03752

Comments

[X, L, G] = care(A, B, Q) solves the continuous-time algebraic Riccati equation.

[X, L, G] = care(A, B, Q, R, S, E) solves the general continuous-time Riccati equation.

Based on the SLICOT library functions SB02OD and SG02AD.