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# gfare

Continuous time filter Riccati equation

### Syntax

[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 |

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