gcare - control Riccati equation

Calling Sequence

[X,F]=gcare(Sl)

Parameters

• Sl : linear system (syslin list)
• X : symmetric matrix
• F : real matrix

Description

Generalized Control Algebraic Riccati Equation (GCARE). X = solution , F = gain.

The GCARE for Sl=[A,B,C,D] is:

(A-B*Si*D'*C)'*X+X*(A-B*Si*D'*C)-X*B*Si*B'*X+C'*Ri*C=0
   

where S=(eye()+D'*D), Si=inv(S), R=(eye()+D*D'), Ri=inv(R) and F=-Si*(D'*C+B'*X) is such that A+B*F is stable.

See Also

gfare