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# h_cl

closed loop matrix

### Syntax

[Acl]=h_cl(P,r,K) [Acl]=h_cl(P22,K)

### Arguments

- P, P22
continuous time linear dynamical systems: augmented plant or nominal plant respectively

- r
a two elements vector, dimensions of 2,2 part of

`P`

(`r=[rows,cols]=size(P22)`

)- K
a continuous time linear dynamical system: the controller

- Acl
real square matrix

### Description

Given the standard plant `P`

(with `r=size(P22)`

) and the controller
`K`

, this function returns the closed loop matrix `Acl`

.

The poles of `Acl`

must be stable for the internal stability
of the closed loop system.

`Acl`

is the `A`

-matrix of the linear system `[I -P22;-K I]^-1`

i.e.
the `A`

-matrix of `lft(P,r,K)`

### See also

- lft — linear fractional transformation

### Authors

F. D.

### 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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