On an invariance principle for differential-algebraic equations with jumps and its application to switched differential-algebraic equations

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.