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Almost rejection of internal structural variations in linear systems

This paper deals with linear systems having internal structural variations. Under some light assumptions, the control of such systems is indeed possible, thanks to the very nice setting of implicit models and Proportional and Derivative (PD) feedbacks. However, the effective design of such PD feedbacks usually requires suitable approximations for the derivatives, hence Proportional approximations of the PD feedback "exact" solution. The aim of the present contribution is to directly table an "almost" version of the problem by pure (high gain) Proportional feedback. The design is different, but very close to the one related to PD feedbacks, mainly with respect to the associated geometric splittings. As an interesting by-product, a system theoretical interpretation of the classical process of "integration by parts" is given and shown to be equivalent to some particular changes of bases.