On Discrete-Time Output Negative Imaginary Systems

This letter introduces the notion of linear Discrete-time Output Negative Imaginary (D-ONI) systems. The D-ONI class is defined in z-domain and it includes systems having poles on unit circle. proposed definition involves a real parameter δ ≥ 0, which indicates strictness properties. > 0 specifies strict subset, Strictly (D-OSNI), within stable class. Interestingly, new captures existing D-NI while restricted to discrete-time LTI real, rational proper transfer function. However, D-OSNI are not identical strictly (D-SNI) subset. Instead, these two subsets intersect each other. An LMI-based state-space characterisation derived check strict/non-strict properties given system relying value δ. paper also establishes connections between Passive NI Finally, closed-loop stability result for positive feedback interconnection without at z = -1 +1.