gcare¶

Continuous time control Riccati equation

Calling Sequence¶

[X,F]=gcare(Sl)

:Sl a continuous time linear dynamical system in state-space: representation

: :X symmetric matrix : :F real matrix :

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.

Version Description 5.4.0 Sl is now checked for continuous time linear dynamical system. This modification has been introduced by this `commit`_ .. _gfare: gfare.html .. _commit: http://gitweb.scilab.org/?p=scilab.git;a=commit;h=3d7083daae3339813ba747c8adcda1f9599bb80d