gcare Continuous time control Riccati equation

## Syntax

    [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

## History

5.4.0 `Sl` is now checked for continuous time linear dynamical system. This modification has been introduced by this commit