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removed >> removed > 6-1-1 > ric_desc

ric_desc

Riccati equation

Syntax

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

Examples

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

See also

History

VersionDescription
6.1.0 ric_desc() is declared obsolete. riccati() replaces it.
6.1.1 ric_desc() will be removed in the next Scilab version.

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