# h_inf

Continuous time H-infinity (central) controller

### Syntax

[Sk, ro] = h_inf(P, r, romin, romax, nmax) [Sk, rk, ro] = h_inf(P, r, romin, romax, nmax)

### Arguments

- P
a continuous-time linear dynamical system ("augmented" plant given in state-space form or in transfer form)

- r
size of the

`P22`

plant i.e. 2-vector`[#outputs,#inputs]`

- romin,romax
a priori bounds on

`ro`

with`ro=1/gama^2`

; (`romin=0`

usually)- nmax
integer, maximum number of iterations in the gama-iteration.

### Description

`h_inf`

computes H-infinity optimal controller for the
continuous-time plant `P`

.

The partition of `P`

into four sub-plants is given through
the 2-vector `r`

which is the size of the `22`

part of `P`

.

`P`

is given in state-space
e.g. `P=syslin('c',A,B,C,D)`

with `A,B,C,D`

= constant matrices
or `P=syslin('c',H)`

with `H`

a transfer matrix.

`[Sk,ro]=H_inf(P,r,romin,romax,nmax)`

returns
`ro`

in `[romin,romax]`

and the central
controller `Sk`

in the same representation as
`P`

.

(All calculations are made in state-space, i.e conversion to state-space is done by the function, if necessary).

Invoked with three LHS parameters,

`[Sk,rk,ro]=H_inf(P,r,romin,romax,nmax)`

returns
`ro`

and the Parameterization of all stabilizing
controllers:

a stabilizing controller `K`

is obtained by
`K=lft(Sk,r,PHI)`

where `PHI`

is a linear
system with dimensions `r'`

and satisfy:

`H_norm(PHI) < gamma`

. `rk (=r)`

is the
size of the `Sk22`

block and `ro = 1/gama^2`

after `nmax`

iterations.

Algorithm is adapted from Safonov-Limebeer. Note that `P`

is assumed to be
a continuous-time plant.

### See also

### Authors

F.Delebecque INRIA (1990)

### 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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