Regularization, Index Reduction, and Generalized Observer Design for Descriptor Systems

This article is focused on the state estimation through generalized observers and index reduction for irregular descriptor systems. Novel sufficient conditions are proposed for the existence of generalized observers of index two. The observers are made in explicit forms through numerically efficient algorithms that are derived by orthogonal transformations on system coefficient matrices. Moreover, through output feedback, the proposed condition has been demonstrated to be both necessary and sufficient for the regularization and index reduction up to index two for square descriptor systems. The given conditions are expressed as algebraic constraints on rank of system matrices and can be easily generalized for higher indexed observers. Real‐world and academic examples demonstrate the observer design and index reduction theory proposed.