Name

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