Figure 1.10. Augmented и problem for robust performance analysis

In the spirit of #oo control, performance is achieved if a closed loop transfer matrix T(s) satisfies a frequency domain template а(ш) at all frequencies u>:

°{T{jш)) < a(u) (1.23)

Assume now the presence of uncertainties in the closed loop, so that T(s) is now an LFT Fi(M(s),A(s)) (i. e. the transfer between w and z in Figure 1.10). Д ( s) is most generally a mixed model perturbation, containing parametric uncertainties and neglected dynamics.

The nominal closed loop is assumed to satisfy the performance property at frequency a>, i. e. :

ff(Fi(W(j’w),0)) < а(ш) (1.24)

The robust performance problem consists in computing the maximal amount of uncertainties, for which closed loop performance is still achieved. The issue is thus to compute the maximal size of the mixed model per­turbation Д ( (s(. for which the following relation holds true:

<f(E,(M(jw), A(ju)) < a(u>) (1.25)

It will be seen in subsection 4.4 that this robust performance prob­lem can be equivalently transformed into an augmented robust stability problem, involving an additional fictitious full complex block (which is called a fictitious performance block). Chapter 7 will moreover illustrate that the robust performance problem is a skewed м problem rather than a classical ц problem.

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