This paper investigates the finite time stability (FTS) of multi-delayed systems with Riemann-Liouville fractional order (RLFO). Firstly, a lemma on the FTS criterion is established for RLFO multi-delay systems, which lays the theoretical groundwork for the subsequent analysis of network synchronization and identification. Secondly, for hybrid coupled complex networks (CNs) with RLFO, multiple delays, and a non-Lipschitz vector field, we explore finite-time synchronization and topology identification (TI) without imposing the linear independence condition (LIC). This is achieved by constructing: (1) a regulated control network with topology observers, and (2) an auxiliary network with isolated nodes. Based on the proposed FTS criterion, along with the designed control protocol and adaptive topology observer, sufficient conditions for the finite time synchronization and TI of multi-delayed CNs are derived as linear matrix inequalities (LMIs). Finally, a numerical simulation on the Lorenz system is carried out to validate the derived results and evaluate the efficacy of the proposed method.
Wang et al. (Fri,) studied this question.