[K,CL,GAM,INFO] = H2SYN(P,NMEAS,NCON)
[K,CL,GAM,INFO] = H2SYN(P,NMEAS,NCON)
computes
a stabilizing H_{2} optimal
controller K
for a partitioned LTI plant P
:
The LTI system P
is partitioned where inputs
to B_{1} are the disturbances,
inputs to B_{2} are the control
inputs, output of C_{1} are
the errors to be kept small, and outputs of C_{2} are
the output measurements provided to the controller. B_{2} has
column size (NCON
) and C_{2} has
row size (NMEAS
). The controller, K
,
is a state-space (ss
) model and has the same
number of states as P
.
If P
is constructed with mktito
, you can omit NMEAS
and NCON
from
the arguments.
The closed-loop system is returned in CL
and
the achieved H_{2} cost γ in GAM
. INFO
is
a struct
array that returns additional information
about the design.
H_{2} control
system CL= lft(P,K)
=.
Output Arguments | Description |
---|---|
K | LTI controller |
CL= lft(P,K) | LTI closed-loop system $$T{y}_{1}{u}_{1}$$ |
GAM = norm(CL) | H_{2} optimal cost γ = $$\begin{array}{l}\Vert {T}_{{y}_{1}{u}_{1}}\Vert 2\\ \end{array}$$ |
INFO | Additional output information |
Additional output — structure array INFO
containing
possible additional information depending on METHOD
)
INFO.NORMS | Norms of four different quantities, full information control cost (FI), output estimation cost (OEF), direct feedback cost (DFL) and full control cost (FC). NORMS = [FI OEF DFL FC]; |
INFO.KFI | Full-information gain matrix (constant feedback) $${u}_{2}(t)={K}_{FI}x(t)$$ |
INFO.GFI | Full-information closed-loop system |
INFO.HAMX | X Hamiltonian matrix (state-feedback) |
INFO.HAMY | Y Hamiltonian matrix (Kalman filter) |
(A, B_{2}, C_{2}) must be stabilizable and detectable.
D_{12} must have full column rank and D_{21} must have full row rank
[1] Safonov, M.G., A.J. Laub, and G. Hartmann, "Feedback Properties of Multivariable Systems: The Role and Use of Return Difference Matrix," IEEE Trans. of Automat. Contr., AC-26, pp. 47-65, 1981.