A behavioural approach to time-varying linear systems, Part 1: General theory

We develop a behavioral approach to linear, time-varying, differential-algebraic systems. The analysis is "almost everywhere" in the sense that the statements hold on R \ T, where T is a discrete set. Controllability, observability, and autonomy are introduced and related to the behavior of the system. Classical results on the behavior of time-invariant systems are studied in the context of time-varying systems