On state space representations of LBR and BR matrices for N-D discrete-time systems and time-delay systems

Sufficient conditions for state space representation of structurally stable N-D bounded real (BR) and lossless bounded real matrices (LBR matrices) are derived in the case of discrete-time systems and noncommensurate time-delay systems. Circuit theoretic interpretations for these conditions are given. The similarity of algebraically equivalent minimal realizations of the 2D LBR transfer function is discussed on the basis of their intermediate realizations in the case of two types of 2D state space model.<
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