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Ajuda do Scilab >> CACSD > Control Design > Linear Quadratic > lqg_ltr

# lqg_ltr

LQG with loop transform recovery

### Syntax

`[kf, kc] = lqg_ltr(sl, mu, ro)`

### Arguments

sl

linear system in state-space form (`syslin` list)

mu,ro

real positive numbers chosen ``small enough''

kf,kc

controller and observer Kalman gains.

### Description

returns the Kalman gains for:

```x = a*x + b*u + l*w1
(sl)
y = c*x + mu*I*w2

z = h*x```

Cost function:

```/+oo
|
J    = E(| [z(t)'*z(t) + ro^2*u(t)'*u(t)]dt)
lqg     |
/ 0```

The lqg/ltr approach looks for `L,mu,H,ro` such that: J(lqg) = J(freq) where

```/+oo        *  *           *
J    =  | tr[S  W  W  S ] + tr[T  T]dw
freq   |
/0```

and

```S = (I + G*K)^(-1)
T = G*K*(I+G*K)^(-1)```

### See also

• syslin — definição de sistemas lineares
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