A SKEWED ц PROBLEM

• With reference to chapter 8 (subsection 2.1), the computation of r(W, ca) at a point (X, ca) is a skewed ц problem, which involves a mixed uncer­tainty A = diag{Ді, Д2) (Ai is here a fictitious full complex block). It is consequently possible to use the first mixed skewed ц bound of chapter 8 (section 1.). Otherwise, the special structure of the problem can be accounted for, and this specific skewed /u problem can be transformed into an augmented p problem: see chapter 8 (section 2.). This solution is easier to implement, since standard p tools are directly available in Matlab Toolboxes (such as the ц Analysis and Synthesis Toolbox or the LMI Control Toolbox).

• A sufficient condition of non-oscillation is used in this section. A skewed Ц upper bound is thus more attractive than a skewed ц lower bound, whose interest is only to measure the conservatism of the upper bound. Indeed, even if a model perturbation A* is obtained, which does not satisfy the sufficient condition of non oscillation, this does not mean that a limit-cycle is obtained when applying A* to the closed loop. On the contrary, the ц upper bound gives a maximal size of the parametric uncertainties, for which the absence of limit-cycle is guaranteed.

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