Velocity-free impulsive consensus for second-order Lipschitz nonlinear multi-agent systems under external disturbances

Abstract

This paper presents novel velocity-free impulsive consensus protocols for second-order multi-agent systems (MASs) subject to Lipschitz nonlinear dynamics, tackling the challenge of distributed impulsive control subject to missing measurements. Unlike existing velocity-dependent strategies, the proposed leaderless framework eliminates velocity reliance through two Lyapunov-based analysis techniques: (i) an augmentation-based Lyapunov technique that is able to fetch the hidden velocity information by exploiting historical sampled position information, and (ii) a Lyapunov-based iterative estimation technique for impulse-delay system to deduce the velocity-free static consensus condition. The robustness of the proposed impulsive consensus protocols against external disturbances is quantified via $H_{\infty }$ performance analysis, allowing the design of robust impulsive control gains with a prescribed level on disturbance attenuation. This velocity-independent framework offers a practical solution for consensus in second-order Lipschitz nonlinear MASs with limited sensing capabilities and environmental disturbances. Numerical simulations validate its effectiveness and theoretical guarantees.