2.4. µANALYSIS 51
2.4.6 State-space Robustness Analysis TestsWewill lo ok at some more advancedstate-space approaches to the analysis of robust
performance. Most users of the software will concentrate on the more commonfrequency
domain analysis methods covered in Section 2.4.3. The analysis tests given here can be
implemented with the Xµfunctions and the more advanced user can use these to study
the robustness of systems with respect to time-varying and nonlinear perturbations.
Toillustrate this approach, consider the state-space LFT model of a system introduced
in Section 2.2.4. A digital system is described by,
x(k+1) = Ax(k)+Bu(k)
y(k)=Cx(k)+Du(k).
This digital system has transfer function,
P(z)=F
u
(P
ss,z−1I),
where Pss is the real valued matrix,
Pss =AB
CD
,
and the scalar ×identity,z−1I, has dimension nx, equal to the sta te dimension of P(z).
This is now in the form of an LFT model with a single scalar ×identity element in the
upper loop.
Define,
∆1=δInxδ∈C,
and note that with this definition,
µ1(A)=ρ(A).