An Intrinsic Behavioural Approach to the Gap Metric

An intrinsic trajectory level approach without any recourse to an algebraic structure of a representation is utilized to develop a behavioural approach to robust stability. In particular it is shown how the controllable behaviour can be constructed at the trajectory level via Zorn´s Lemma, and this is utilized to study the controllable-autonomous decomposition. The gap distance is generalised to the behavioural setting via a trajectory level definition; and a basic robust stability theorem is established for linear shift invariant behaviours.