ric_desc - Riccati equation

Calling Sequence

X=ric_desc(H [,E))

[X1,X2,zero]=ric_desc(H [,E])

Parameters

• H,E : real square matrices
• X1,X2 : real square matrices
• zero : real number

Description

Riccati solver with hamiltonian matrices as inputs.

In the continuous time case calling sequence is (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 (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

riccati