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

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... lays and fully determined by the system matrices. The validity of the theoretical results is demonstrated by a numerical example. Fig. 2 Output trajectory of system (1) under input w(t) = 1