“Staircase phenomenon” in delay-independently stable networked control system's dynamic response: Discrete-time case

This paper mainly deals with the issue of “staircase phenomenon” of delay-independently stable networked control systems (NCSs). There already exist works on this topic in continuous-time domain, this paper extends the former result and deals with the more realistic discrete-time case. The definition of “staircase phenomenon” is given at first and the reason is analyzed. Then it is proven that if a NCS with traditional feedback structure is delay-independently stable, then “staircase phenomenon” in its dynamic response cannot be eliminated. This paper proceeds to prove that if a NCS which is delay-independently stable is introduced with scattering transformation, then its steady state error and “staircase phenomenon” in its dynamic response can be eliminated altogether by tuning the parameter of the transformation.