ric_desc - Riccati equation
Riccati solver with hamiltonian matrices as inputs.
In the continuous time case calling sequence is ric_descr(H) (one input):
Riccati equation is:
(Ec) A'*X + X*A + X*R*X -Q = 0.
Defining the hamiltonian matrix H by:
H = [A R;
Q -A']
with the calling sequence [X1,X2,zero]=ric_descr(H) , the solution X is given by X=X1/X2 .
zero = L1 norm of rhs of ( Ec )
The solution X is also given by X=riccati(A,Q,R,'c'))
In the discrete-time case calling sequence is ric_descr(H,E) (two inputs):
The Riccati equation is:
(Ed) A'*X*A-(A'*X*B*(R+B'*X*B)^-1)*(B'*X*A)+C-X = 0.
Defining G=B/R*B' and the hamiltonian pencil (E,H) by:
E=[eye(n,n),G; H=[A, 0*ones(n,n);
0*ones(n,n),A'] -C, eye(n,n)];
with the calling sequence [X1,X2,err]=ric_descr(H,E) , the solution X is given by X=X1/X2 .
zero = L1 norm of rhs of ( Ed )
The solution X is also given by X=riccati(A,G,C,'d') with G=B/R*B'
riccati ,