Stabilization of Switched Linear Differential Algebraic Equations and Periodic Switching

We investigate the stabilizability of switched linear systems of differential-algebraic equations (DAEs). For such systems we introduce a parameterized family of switched ordinary differential equations that approximate the dynamic behavior of the switched DAE. A necessary and sufficient criterion for the stabilizability of a switched DAE system using time-dependent switching is obtained in terms of these parameterized approximations. Furthermore, we provide conditions for the stabilizability of switched DAEs via fast switching as well as using solely the consistency projectors of the constituent systems. The stabilization of switched DAEs with commuting vector fields is also analyzed.