lqg2stan(1)

NAME
lqg2stan - LQG to standard problem

CALLING SEQUENCE
[P,r]=lqg2stan(P22,bigQ,bigR)

PARAMETERS

P22 : syslin list (nominal plant) in state-space form

bigQ
    : [Q,S;S',N] (symmetric) weighting matrix

bigR
    : [R,T;T',V] (symmetric) covariance matrix

r   : 1x2 row vector = (number of measurements, number of inputs) (dimension of
     the 2,2 part of P)

P   : syslin list (augmented plant)

DESCRIPTION
lqg2stan returns the augmented plant for linear LQG (H2) controller design.

P22=syslin(dom,A,B2,C2) is the nominal plant; it can be in continuous time (dom='c') or discrete time (dom='d').
  .
  x = Ax + w1 + B2u
  y = C2x + w2
for continuous time plant.
  x[n+1]= Ax[n] + w1 + B2u
      y = C2x + w2
for discrete time plant.

The (instantaneous) cost function is [x' u'] bigQ [x;u].

The covariance of [w1;w2] is E[w1;w2] [w1',w2'] = bigR

If [B1;D21] is a factor of bigQ, [C1,D12] is a factor of bigR and [A,B2,C2,D22] is a realization of P22, then P is a realization of [A,[B1,B2],[C1,-C2],[0,D12;D21,D22]. The (negative) feedback computed by lqg stabilizes P22.

EXAMPLE
ny=2;nu=3;nx=4;
P22=ssrand(ny,nu,nx);
bigQ=rand(nx+nu,nx+nu);bigQ=bigQ*bigQ';
bigR=rand(nx+ny,nx+ny);bigR=bigR*bigR';
[P,r]=lqg2stan(P22,bigQ,bigR);K=lqg(P,r);  //K=LQG-controller
spec(h_cl(P,r,K))      //Closed loop should be stable
lqg2stan(1/(s+2),eye(2,2),eye(2,2))

SEE ALSO
lqg, lqr, lqe, obscont, h_inf, augment, fstabst

AUTHOR
F.D.