Stability and [formula omitted]-gain of positive fractional-order coupled differential-difference systems with unbounded time-varying delays

Abstract

This work aims to research the positivity, stability, and L∞-gain of incommensurate fractional-order coupled differential-difference systems (FOCDDSs) with unbounded time-varying delays. By virtual of the Banach’s fixed point theorem, the existence and uniqueness of the solution of FOCDDs is given. A necessary and sufficient criterion ensuring the positivity of delayed FOCDDSs is put forward. Then, by analyzing the monotonicity of system trajectories and constructing sample data systems, a necessary and sufficient criterion realizing the stability of positive FOCDDSs is obtained. Different from related works, there is no need to require the Lyapunov–Krasovskii function or the comparison between the counterpart with constant time delays by the proposed approach. To obtain the L∞-gain of FOCDDSs, two auxiliary systems are developed to calculate the limit of the state trajectory. Eventually, a numerical experiment is performed to verify the rationality of the results.