THE GENERAL CASE

We now consider the general case of a closed loop, which is simul­taneously subject to parametric uncertainties and neglected dynamics.

The issue is first to realize the parametrically uncertain plant model as an LFT Fi(H(s), Д3) (see subsection 1.4). The control law is then con­nected with the plant and the neglected dynamics are finally added at various locations of the closed loop. The standard interconnection struc­ture M{s) — A(s) is obtained, by noting that M(s) is the transfer matrix seen by the structured model perturbation A(s).

II’2

Figure 1.7. Computation of the standard interconnection structure

The example of Figure 1.7 combines the examples of figures 1.6 and 1.4. The parametric uncertainties are gathered in Д3 = diag(SiIqi). Д(з) has the following structure:

A(s) = diag(Ai(s),A2(s),S1Iqi,… ,SrIqr) (1.16)

whereas M(s) is the transfer matrix between (w,W2,w^) and outputs (zi, z2, z3).