LQG to standard problem
[P_aug, r] = lqg2stan(P, Qxu, Qwv)
State space representation of the nominal plant (nu
inputs, ny
outputs, nx
states).
[Q, S ; S', N]
symmetric nx+nu
by
nx+nu
weighting matrix.
[R,T;T',V]
symmetric nx+ny
by
nx+ny
covariance matrix.
Row vector [ny nu]
.
Augmented plant state space representation (see: syslin)
lqg2stan
returns the augmented plant for linear LQG (H2) controller
design problem defined by:
The nominal plant P
: described by
The (instantaneous) cost function
.
The noises covariance matrix
If [B1; D21]
is a factor of
Qxu
, [C1, D12]
is a
factor of Qwv
(see: fullrf) then
P_aug = syslin(P.dt, P.A, [B1,P.B], [C1;-P.C], [0,D12;D21,P.D])
ny = 2; nu = 3; nx = 4; P = ssrand(ny,nu,nx); Qxu = rand(nx+nu,nx+nu); Qxu = Qxu * Qxu'; Qwv = rand(nx+ny,nx+ny); Qwv = Qwv * Qwv'; [P_aug, r] = lqg2stan(P, Qxu, Qwv); K = lqg(P_aug,r); // K=LQG-controller spec(h_cl(P_aug, r, K)) // Closed loop should be stable //Same as Cl = P/.K; spec(Cl('A')) lqg2stan(1/(%s+2), eye(2,2), eye(2,2)) | ![]() | ![]() |
Version | Description |
6.0 | It is no longer necessary to enter -P to get P_aug
instead of -P_aug
(bug 13751 fixed). |