On some properties of N-D discrete-time BR systems and time-delay BR systems

Based on N-D state equations, we present sufficient condition for N-D discrete-time systems to be structurally stable bounded real (BR) and its circuits theoretical interpretations. N-D discrete-time systems satisfying this condition can be embedded into a certain augmented lossless bounded real (LBR) system and energy balanced realization is possible. These results can be extended straightforward to time-delay systems which are BR independent of delay. But in the case BR property is dependent on delay, such extension is impossible