Invariance principles for switched Differential-Algebraic Equations under arbitrary and dwell-time switching

We investigate the invariance properties of a class of switched systems in which 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 for such 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 and generate invariance principles for such switched systems. Examples are included to illustrate the results.