Invariance principles and passivity notions for switched DAE and hybrid DAE systems (2017)
Homogeneous and non-homogeneous linear switched differential algebraic equations (DAE) are studied. Particularly, a class of switched system where the vallle of a switching signal determines the current model of operation (among a finite number of them) and, for each mode, its dynamics are described by a DAE. Also, we consider a class of hybrid dynamical system with continllous dynamics that can be modeled as DAEs and with discrete dynamics given by difference inclusions. We denote such class of hybrid systems as hybrid DAE systems. Motivated by the lack of invariance principles and input-output analysis (such as passivity) for switched DAE systems, a main goal of this dissertation is the stability analysis of both switched DAE and hybrid DAE systems through invariance properties and passivity concepts