On Homogeneous Descriptor Systems and Homogeneity-Based Finite-Time Control of Linear Descriptor Systems

Abstract

A new definition of homogeneity for descriptor systems is introduced. The homogeneity property can be verified algebraically, and, as for systems described by ordinary differential equations only, it implies scalability of solutions. A finite-time stabilizing feedback controller is designed for linear descriptor systems. The proposed control contains a homogenizing linear feedback term and a nonlinear homogeneous stabilizing term. The parameters tuning is presented in the form of linear matrix equations and inequalities. Performance of the approach is illustrated by numerical examples.