On a useful family of difference operators for short time intervals, and some isometries of spaces of linear systems

For linear dynamical systems with time interval length ??, 0 ?? ?? ?? 1, a representation with a new difference/ differential operator ???? is presented, which interpolates between the usual discrete time representation (??=1) and the usual continuous time representation (??=0). For this representation the stability region is studied, the l2/L2-norm is defined and several formulas are presented, and investigation of the ????-operator leads to interesting classes of isometries of spaces of linear systems.