riccati

Arguments

A,B,C

real matrices nxn, B and C symmetric.

dom

'c' or 'd' for the time domain (continuous or discrete)

typ

string : 'eigen' for block diagonalization or schur' for Schur method.

X1,X2,X

square real matrices (X2 invertible), X symmetric

Description

X=riccati(A,B,C,dom,[typ]) solves the Riccati equation:

A'*X+X*A-X*B*X+C=0

in continuous time case, or:

A'*X*A-(A'*X*B1/(B2+B1'*X*B1))*(B1'*X*A)+C-X

with B=B1/B2*B1' in the discrete time case. If called with two output arguments, riccati returns X1,X2 such that X=X1/X2.

Examples

// Continuous
n = 10;
A = rand(n,n);
B = rand(n,n);
C = rand(n,n);
C = C*C';
R = rand(n,n);
R = R*R'+eye();
B = B*inv(R)*B';

X = riccati(A,B,C,'c','eigen')

// Discrete

n = 10;
F = rand(n,n);
G1      = rand(n,n);
G2 = rand(n,n);
G2 = G2*G2'+eye();
G      = G1/G2*G1';
H      = rand(n,n);
H = H*H';

[X1,X2]= riccati(F,G,H,'d','schur')

See also

• ricc — Riccati equation
• ric_desc — Riccati equation
• srfaur — square-root algorithm
• lindquist — Lindquist's algorithm