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Aide de Scilab >> CACSD (Computer Aided Control Systems Design) > gcare

gcare

Continuous time control Riccati equation

Calling Sequence

[X,F]=gcare(Sl)

Arguments

Sl

a continuous time linear dynamical system in state-space representation

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 — Continuous time filter Riccati equation

History

VersionDescription
5.4.0 Sl is now checked for continuous time linear dynamical system. This modification has been introduced by this commit
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Copyright (c) 1989-2007 (ENPC)
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Last updated:
Thu Oct 02 13:54:31 CEST 2014