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# 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 — Continuous time filter 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 |

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