<inline-formula> <tex-math notation="LaTeX">$\ell_\infty$ </tex-math></inline-formula>-Gain Analysis of Discrete-Time Positive Singular Systems With Time-Varying Delays

• Main Authors: Yukang Cui, Hao Feng, Guang-Zhong Cao
• Format: Article
• Language: English
• Published: IEEE 2019-01-01
• Series: IEEE Access
• Subjects: Positive systems; singular systems; time-delay; <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">ℓ</italic>∞-gain
• Online Access: https://ieeexplore.ieee.org/document/8853250/
• ISSN: 2169-3536

This paper is concerned with the &#x2113;_&#x221E;-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 &#x2113;_&#x221E;-gain of discrete-time singular systems with time-varying delays is given in terms of system matrices. The result shows that &#x2113;_&#x221E;-gain of discrete-time positive singular systems with bounded time-varying delays is insensitive to the magnitude of delays.