On stability of time-varying linear differential-algebraic equations
We develop a stability theory for time-varying linear differential algebraic equations (DAEs). Standard stability concepts for ODEs are formulated for DAEs and characterized. Lyapunov’s direct method is derived as well as the converse of the stability theorems. Stronger results are achieved for DAEs which are transferable into standard canonical form; in this case the existence of the generalized transition matrix is exploited.