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This paper proposes notions and a tool for passivity properties of non-homogeneous switched Differential Algebraic Equation (DAE) systems and their relationships with stability and control design. Motivated by the lack of results on input-output analysis (such as passivity) for switched DAE systems and their interconnections, we propose to model non-homogeneous switched DAE systems as a class of hybrid systems, modeled here as hybrid DAE systems with linear flows. Passivity and its variations are defined for switched DAE systems and methods relying on storage functions are proposed. The main contributions of this paper are: 1) passivity and detectability concepts for switched DAE systems, 2) links of the aforementioned passivity and detectability properties to stabilization via static output-feedback. Our results are illustrated in a power system, namely, the DC-DC boost converter, whose model involves DAEs and requires feedback control.

We investigate the invariance properties of a class of switched systems where the value of a switching signal determines the current mode of operation (among a finite number of them) and, for each fixed mode, its dynamics are described by a Differential-Algebraic Equation (DAE). Motivated by the lack of invariance principles of switched DAE systems, we develop such principles for switched DAE systems under arbitrary and dwell-time switching. By obtaining a hybrid system model that describes the switched DAE system, we build from invariance results, for hybrid systems, the invariance principles for such switched systems. Examples are included to illustrate the results.