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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:

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'`

### Examples

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

### See also

- riccati — Riccati equation

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