Robust performance against time-varying structured perturbations
Poola, K.; Tikku, A.
Automatic Control, IEEE Transactions on
Volume 40, Issue 9, Sep 1995 Page(s):1589 - 1602
Digital Object Identifier 10.1109/9.412628
Summary:In this paper, we consider the problem of robust performance
analysis for some nominal system M(z) against bounded, linear,
time-varying, structured feedback perturbations. We introduce a natural
input-output notion of rate-of-variation for a linear time-varying
operator. We then exhibit upper and lower bounds on the maximum
rate-of-variation of these perturbations against which robust
performance is achievable. Using these bounds, we show that the
existence of frequency dependent D-scales that render the norm of M(z)
less than one is necessary and sufficient for robust performance against
arbitrarily slowly varying structured linear perturbations of norm less
than one. This result suggests that it is natural and well justified to
deal with the frequency-dependent upper bound for the μ
“norm,” rather than μ itself. This is reassuring given
that the upper bound is easily and reliably computable, while
computation of complex μ appears difficult
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