lqg_ltr

Scilab Function
Last update : 12/01/2004

lqg_ltr - LQG with loop transform recovery

### Calling Sequence

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

### Parameters

- `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`,