Parameters

Description

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'

See Also