Multi-model/multi-objective state-feedback synthesis
[gopt,h2opt,K,Pcl,X] = msfsyn(P,r,obj,region,tol)
Given an LTI plant
P with state-space equations
msfsyn computes a state-feedback control
u = Kx that
Maintains the RMS gain (H∞ norm) of the closed-loop transfer function T∞ from w to z∞ below some prescribed value γ0 > 0
Maintains the H2 norm of the closed-loop transfer function T2 from w to z2 below some prescribed value υ0 > 0
Minimizes an H2/H∞ trade-off criterion of the form
Places the closed-loop poles inside the LMI region specified by
lmiregfor the specification of such regions). The default is the open left-half plane.
r = size(d22) and
obj = [γ0, ν0, α, β] to specify the problem dimensions and the design parameters γ0, ν0, α, and β. You can perform pure pole placement by setting
obj = [0 0 0 0]. Note also that z∞ or z2 can be empty.
h2opt are the guaranteed H∞ and H2 performances,
K is the optimal state-feedback gain,
Pcl the closed-loop transfer function from w to , and
X the corresponding Lyapunov matrix.
msfsyn is also applicable to multi-model problems where
P is a polytopic model of the plant:
with time-varying state-space matrices ranging in the polytope
In this context,
msfsyn seeks a state-feedback gain that robustly enforces the specifications over the entire polytope of plants. Note that polytopic plants should be defined with
psys and that the closed-loop system
Pcl is itself polytopic in such problems. Affine parameter-dependent plants are also accepted and automatically converted to polytopic models.