$\ell_\infty$ -Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays

This paper is concerned with the ℓ_∞-gain analysis problem of discrete-time positive singular systems with time-varying delays. By introducing an auxiliary system, a necessary and sufficient positivity condition is proposed for systems. Then, by using of the positivity and linearity, we investigate the monotonic and asymptotic property of the system with time-varying delays. Then, by resorting to the comparing system with constant delays, an explicit expression of the ℓ_∞-gain of discrete-time singular systems with time-varying delays is given in terms of system matrices. The result shows that ℓ_∞-gain of discrete-time positive singular systems with bounded time-varying delays is insensitive to the magnitude of delays.