'Staircase phenomenon' in delay independently stable networked control system's dynamic response

When networked control systems (NCSs) are stable with any constant time delays, then they are delay-independently stable. Many works in the literature are concerned with this stability concept, giving different criterions for it. This study mainly deals with the dynamic performance of such systems and discusses the issue of 'staircase phenomenon'. The definition of 'staircase phenomenon' is given at first and it is demonstrated that existence of 'staircase phenomenon' usually means that the system's dynamic process is slow. Then it is proven that if a NCS with traditional feedback structure is delay-independently stable, then the 'staircase phenomenon' in its dynamic response cannot be eliminated. This is an inner restriction of delay-independently stable NCS under traditional feedback structures, which can only be broken by changing the system's structure. It is already proven in the literature that the introduction of scattering transformation into NCS can bring profound changes to the system's structure. This study 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. Simulation result is provided at the end.