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# ric_desc

Riccati equation

### Syntax

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

### Arguments

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, the syntax 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 syntax [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, the syntax 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 syntax [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'

h=[0.5,4;
0,-0.5]
x=ric_desc(h)