By Jack David
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O ° . ~ ° ° ~ ° ~ ° ° . . . oo° . . . w ~ o o o o . o o o . . . . . ° H ~ - ° * ~ - ' ~ ' ~ * ~ ° ~ ° ~ ° ~ ° ~ ° ~ ° ~ ° * ° ° ~ ' ' - * ° ° ° ° ~ ° ° ° ~ ° * ° ~ ° ° ~ * ~ * ° ° ~ - ~ ° ~ - ° ~ ` ~ . 1 The Normalized L C F Robust Stabilization Problem 'Let (IV, 2(¢) be a normalized left coprime factorization of G. ~), such that GA = (/'1}/"+ A M ) - I ( / ~ + AN) can be stabilized by a single controller, K , for all A E DC~ is given by e.... 3) where K is chosen over all stabilizing controllers.
I t ]W1 idI "I I z -I i L~ ....... I w ,! ~ i P :i +( ;' z l P 2 I + L J u i i! ooooo.. . . . . o o . . ~ . . . . . . . . . . . . . . . 12. ,i,, exactly, and we will consider an iterativc procedure here. For this purpose we introduce the so called Sub-Optimal Hoo Problem, that of finding a stabilizing controller, K , such that for 7 > 7-~in, II~'KP, K)Iloo < 7. 11), and parametrize all such controllers. We review this work next, and then outline an iterative procedure for estimating %,a,,.
1 Background For the presence of modelling error to play a part in controller analysis and design, it is necessm'y to construct some form of mathematical model to represent the error. The modelling should be based on the information available about the uncertainty, or, if this is unavailable, on reasonable assumptions about its magnitude. A key assumption in all modelling of system errors is that the uncertain part of a process can bc modelled separately from the known part of the process, as represented by the nominal model.