Observer-based resilient PD-like scaled group consensus for uncertain multiagent systems under time-varying delays

This paper addresses the issue of observer-based resilient scaled group consensus control for uncertain nonlinear multiagent systems subject to delays and disturbances. First, a distributed observer is introduced for each uncertain agent, enabling precise estimation of both the state and disturbance, while tolerating variations in observer gain. Next, a resilient proportional-derivative-like scaled group consensus protocol is formulated, accounting for both the observer and communication delays. Notably, this protocol achieves scaled group consensus while enhancing performance. A new delay-product type Lyapunov-Krasovskii functional is then developed, incorporating terms for triple integrals and Bessel-Legendre vectors, unlike the traditional quadratic form. By applying the Bessel-Legendre inequality and the extended reciprocally convex matrix inequality, new sufficient conditions for scaled group consensus are derived, yielding reduced conservatism. Finally, numerical examples are provided to validate the theoretical findings.