On “verticum”-type linear systems with time-dependent linkage

Abstract “Verticum”-type linear systems with time-dependent coupling are particular time-dependent systems consisting of subsystems such that the temporal output of the i -th subsystem is one of the inputs of the consecutive subsystem. Kalman's type rank conditions are proved for the controllability and the observability of these systems under a very simply expressed differential-algebraic condition for the time-dependent coefficients.