Filter
Top Products
270 Chapter 6. Function Reference
p
k
-
zw
y
u
The variables ncon and nmeas are used to specify the dimensions of u and y in the above
diagram (ncon = dim(u)andnmeas = dim(y)). The objective is to design a stabilizing
controller, k, which minimizes the H
2
norm of the closed loop system between w and z.
p is a state-space system, which can be partitioned with respect to [z; y]and[w;u]in
the following way.
p =
a
b
1
b
2
c
1
d
11
d
12
c
2
d
21
d
22
.
The following assumptions must hold:
1. (a,b
2
,c
2
) is stabilizable and detectable
2. d
12
and d
21
have full rank
3. d
11
=0
4. The matrix [a − jωI,b
2
;c
1
,d
12
] has full column rank for all ω
5. The matrix [a − jωI,b
1
;c
2
,d
21
] has full row rank for all ω
In theory the Riccati equations should always have a solution. However, Hamiltonian
eigenvalues which are close to the imaginary axis will give problems. epr specifies a
tolerance for how close the calculated eigenvalues can be to the jω axis.