Bohl exponent for time-varying linear differential-algebraic equations

We study stability of linear time-varying differential-algebraic equations (DAEs). The Bohl exponent is introduced and finiteness of the Bohl exponent is characterised, the equivalence of exponential stability and a negative Bohl exponent is shown and shift properties are derived. We also show that the Bohl exponent is invariant under the set of Bohl transformations. For the class of DAEs which possess a transition matrix introduced in this article, the Bohl exponent is exploited to characterise boundedness of solutions of a Cauchy problem and robustness of exponential stability.