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# 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 — linear system definition

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