Controllability of Multiparameter Singularly Perturbed Systems.

Abstract

The controllability of a general linear time-invariant multiparameter singularly perturbed system is studied with no a priori assumptions on the relative magnitudes of the small parameters. It is shown how Kokotovic and Haddad's result on persistence of controllability under singular perturbations in the single parameter case extends to this more general setting. The separation of the system eigenvalues into 'slow' end 'fast' groups is proved here for the first time and employed in the analysis. It is found that one does not expect controllability for all sufficiently small values of the parameters, but conditions are given for this property to hold for almost all sufficiently small values of the small parameters. Moreover, one can describe the set in parameter space for which the system is not controllable.