Stability and ℓ ∞ ‐gain analysis for discrete‐time positive singular systems with unbounded time‐varying delays

This study considers the stability and ℓ ∞ ‐gain analysis problem for discrete‐time positive singular systems with unbounded time‐varying delays. By proposing some new techniques and employing mathematical induction method, the authors first derive a sufficient condition to analyse the stability of the system. The authors then investigate the ℓ ∞ ‐gain by exploiting the monotonicity of state trajectory. They show that the ℓ ∞ ‐gain for the considered systems is independent of the magnitude of delays and fully determined by the system matrices. The validity of the theoretical results is demonstrated by a numerical example.