Continuous Time-Varying Scalar Systems - a Behavioural Approach

Abstract

We introduce a behavioural approach to linear time-varying systems p( d dt )w 1 = q( d dt )w 2 , where p(D); q(D) belong to M[D], i.e. the skew polynomial ring with real meromorphic coefficients M, indeterminate D, and multiplication rule Df = fD+ f . Willem's behavioural approach to time-invariant systems and approaches to timevarying systems are generalized. We are aiming at a global approach in the sense that the time axis consists of the real numbers minus a discrete set of critical points where the solutions of thesystem may exhibit finite escape time. Controllable and autonomous behaviours are introduced and characterized. Institute of Mathematics, Technical University Ilmenau, Weimarer Strae 25, 98693 Ilmenau, FRG, [email protected] y Department of Electrical and Electronic Engineering, The University of Melbourne, Parkville, Victoria 3052, Australia, kuang,m.kuijper,[email protected] Nomenclature A the set of real analytic functions f : R ! R M ..