Consensus Control for PDE-ODE MASs With Multi Delays: A Dual-Mode Adaptive Event-Triggered Strategy and Novel Stability Analysis Criterion

Consensus in fractional-order multi-agent systems (MASs) with time delays has attracted considerable research interest in recent years. Numerous existing findings rely heavily on the stability theory of fractional-order delay systems. In these findings, however, certain stability rates remain inestimable, while others lack rigorous estimation. This paper develops enhanced Mittag-Leffler stability criterion for fractional-order systems incorporating infinite distributed and discrete delays, which provides precise characterizations of convergence rates and establish a pioneering framework for fractional-order stability analysis. Moreover, this work proposes a novel dual-mode adaptive event-triggered strategy (DMAETS) to optimize limited communication resources and enhance network utilization efficiency. The DMAETS framework features time-varying event-triggering thresholds and adaptive control gains that dynamically adjust based on real-time system states. Through innovative DMAETS-based controller designs (internal/boundary configurations) and the proposed stability criterion, the fractional-order coupled PDE-ODE MASs (FCPOMASs) achieve consensus, with corresponding consensus conditions derived as linear matrix inequalities (LMIs). Finally, two simulation examples are presented to illustrate the validity of the theoretical analysis and the feasibility of the control schemes.