gfare

Continuous time filter Riccati equation

Calling Sequence

[Z,H]=gfare(Sl)

Arguments

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

representation

: :Z symmetric matrix : :H real matrix :

Description

Generalized Filter Algebraic Riccati Equation (GFARE). Z = solution, H = gain.

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

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

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

See Also

• `gcare`_ Continuous time control Riccati equation

History

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