dlyapchol
Solves discrete-time Lyapunov equations with a square-root solver.
Syntax
X = dlyapchol(A, B)
X = dlyapchol(A, B, E)
Inputs
- A
- Real square matrix.
- B
- A real matrix.
- E
- Real square matrix.
Outputs
- X
- A real matrix.
Examples
Example based on a Lyapunov matrix equation:
A = [-5.0 0 -5.0;
0.5 0 0;
0 0 0.5];
B = [ 0.5 1 0.5;
1.5 1 1;
1 1 1.5];
U1 = dlyapchol (A, B)U1 = [Matrix] 3 x 3
0.50000 1.50000 1.00000
1.00000 1.00000 1.00000
0.50000 1.00000 1.50000Example based on a Sylvester equation:
A = [-5.0 0 -5.0;
0.5 0 0;
0 0 0.5];
B = [ 0.5 1 0.5;
1.5 1 1;
1 1 1.5];
E = [2 2 4;
1 0 5;
3 1 1];
U2 = dlyapchol (A, B, E)U2 = [Matrix] 3 x 3
0.50000 1.50000 1.00000
1.00000 1.00000 1.00000
0.50000 1.00000 0.00000Comments
R = dlyapchol(A, B) solves AU'UA' - U'U = -BB' (Lyapunov matrix equation).
X = dlyapchol(A, B, E) solves AU'UA' - EU'UE' = -B B' (Sylvester equation).
Based on the SLICOT library functions SB03OD and SG03BD.