  The problem of state reconstruction and estimation is considered for a class
of switched dynamical systems whose subsystems are modeled using linear
differential-algebraic equations (DAEs). Since this system class imposes
time-varying dynamic and static (in the form of algebraic constraints)
relations on the evolution of state trajectories, an appropriate notion of
observability is presented which accommodates these phenomena. Based on this
notion, we first derive a formula for the reconstruction of the state of the
system where we explicitly obtain an injective mapping from the output to the
state. In practice, such a mapping may be difficult to realize numerically and
hence a class of estimators is proposed which ensures that the state estimate
converges asymptotically to the real state of the system.
