lqg_ltr

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