Stability and <i>l</i>_∞ Performance Analysis for Nabla Discrete Fractional Linear Positive System with Time-Varying Delays

Abstract

In this paper, the stability and l∞-gain problem are investigated for the Nabla discrete fractional linear positive systems with bounded time-varying delays. First, a sufficient condition and a necessary condition are presented to ensure the system’s positivity. Then, based on the system’s positivity property, an asymptotically stable condition is established. Furthermore, it is demonstrated that the l∞-gain of such systems is determined by the system matrices and is independent of the magnitude of delays. Finally, numerical examples are provided to demonstrate the validity of the obtained results.

Keywords

• nabla discrete fractional system
• positive system
• time-varying delay
• stability
• <i>l</i>∞ performance