For high frequency noise, a new $2n$-th order cascade extended state observer with dynamic dead-zone structure is proposed in this paper. Dead zone dynamic consists of two parts. One is to "trim" the effect of noise by cutting off the part that falls in the dead zone. The other part pushes the dead zone amplitude to converge to 0 as soon as possible to ensure the convergence of the estimation error. Moreover, in the cascade structure, the high-gain parameter grows only to a second power, thus avoiding excessive amplification of the measurement noise and solving numerical implementation problems. The design procedure ensures that the extended state observer is input-to-state stable. Numerical simulations show the improvement in terms of total disturbance estimation and noise attenuation. The frequency-domain analysis of the proposed ESO using the describing function method investigates the effect of the dead zone nonlinear parameter on the performance of a closed-loop system.

This study presents a modified Cucker-Smale system with external perturbation and intermittent control. First, a new finite-time stability lemma is developed, in which the settling time is determined only by the control interval's duration. Second, by imposing an assumption on external perturbation, the system can achieve collision-avoidance flocking. Third, finite-time flocking is achieved without the sign function, which effectively avoids the undesirable chattering phenomenon in the system. Finally, numerical simulations validate the theoretical analysis, and parameter sensitivity analysis offers important guidance for practical applications such as unmanned aerial vehicle (UAV) formations.