Regularity of DAEs as described in Part I is supported by several constant-rank conditions. In the present chapter we relax these conditions and allow for rank changes. Replacing the nullspaces of the admissible matrix functions by continuous subnullspaces we again obtain continuous matrix function sequences. These modified sequences inherit most of the properties given for the standard sequences in Part I. By this, we figure out so-called quasi-regular DAEs. In particular, linear DAEs that are transformable into so-called standard canonical form belong to quasi-regular DAEs. A decoupling procedure applied to general linear quasi-regular DAEs is offered. Unfortunately, the rank values serving as characteristic values within the regularity concept in Part I now lose their meaning. Similarly to the mostly applied differentiation index notion, quasi-regularity appears to be somewhat diffuse. We touch on difficulties arising with the use of subnullspaces.
KeywordsMatrix Function Projector Function Constant Rank Tractability Index Continuous Subspace
Unable to display preview. Download preview PDF.