Leader‐following consensus for fractional‐order multi‐agent systems with uncertainty and mixed time delays

Abstract This paper examines leader‐following consensus for fractional‐order multi‐agent systems ( ) with structured multiplicative norm‐bounded uncertainties and mixed time delays. The system dynamics are modelled using the Caputo fractional derivative, chosen because it retains the physical meaning of initial conditions and works with the Lyapunov–Razumikhin stability analysis. The mixed delays considered here include state delays (discrete or distributed) and input (communication) delays, treated as fixed constants. Formulating a proper fractional‐order Razumikhin–Lyapunov function and incorporating the uncertainty bound into the analysis, delay‐dependent agreement criteria are obtained as decoupled linear matrix inequalities (LMIs) in the case of discrete‐time delay as well as distributed delay. Moreover, we also give similar spectral‐radius results that simplify the computation, replacing large dimensions LMIs with smaller scaling eigenvalue checks. Numerical examples demonstrate the feasibility of the conditions, highlight robustness improvements compared to existing methods, and illustrate trade‐offs between convergence speed, uncertainty tolerance, and computational burden.