96 CHAPTER 3. FUNCTIONAL DESCRIPTION OF Xµ
Figure 3.5: Interconnection structure for controllersynthesis
structure contains more than just the open loop plant. It typically also contains
frequency dependent weighting functions and specifies the structure of the
interconnection between the open loop plant and the controller. The dimensions of y
and uare specified by nmeas and ncon. The underlying Riccati equations can be solved
by either an eigenvalue or Schurdecompos ition method. A keyword specifies the desired
Riccati solution method. A simple is example is given at the end ofthis section.
The hinfsyn function calculates a controller, K(s), which makes kG(s)k∞≤γforauser
specified γ. It is not possible to make γarbitrarily small; there is a minimum value for γ
(referred to as γopt)andγ
opt is not known a priori in a design problem. Therefore
hinfsyn can also perform a bisection search for the smallest γ>γ
opt and use this value
of γfor the control design. Again, Section 2.3 gives the relevant theoretical details.
The syntax of hinfsyn is illustrated below. The final bound o n the achievedγis
returned as gfin.
[k,gfin] = hinfsyn(p,nmeas,ncon,gamma)
If gamma is a scalar, the controller achieving that γvalue is calculated, if one exists. If
gamma is a two elementvector a bisection search for the smallest γvalue is performed.
The function displays various intermediate calculations related to the eigenvalues of the
Hamiltonian and the positivity of the Riccati solutions. As γapproaches γopt the Riccati