Riccati equation
X = ric_desc(H) X = ric_desc(H, E) [X1, X2, zero] = ric_desc(H) [X1, X2, zero] = ric_desc(H, E)
real square matrices
real square matrices
real number
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'
Version | Description |
6.1.0 | ric_desc() is declared obsolete.
riccati() replaces it. |
6.1.1 | ric_desc() will be removed in the next Scilab version. |