A behavioural approach to time-varying linear systems, Part 2: Descriptor systems

In the sequel to [A. Ilchmann and V. Mehrmann, SIAM J. Control Optim., 44 (2005), pp. 1725–1747], we discuss a behavioral approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is "almost global" in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the "time axis" R \ T, where T is a discrete set of critical points, at which the solution may exhibit a finite escape time. Controllable, observable, and autonomous behavior for linear time-varying descriptor systems is characterized