Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Abstract

In this paper, finite-time stabilization of coupled systems on networks with time-varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self-delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite-time stabilization of coupled oscillators with time-varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.

Dynamic stability of a class of fractional‐order nonlinear systems via fixed point theory

“…17 Recently, this method has been favored by many scholars and developed rapidly. [18][19][20][21][22] In their study, Chen et al 23 presented a robust stability of fractional-order linear delayed system with nonlinear perturbations over a finite-time interval. In Wu et al, 24 a class of fractional-order delayed neural networks was considered.…”

Finite‐time stabilization of maglev system with an output constraint

“…where 𝜇 0 is the permeability of vacuum, N is coil turns, S is the effective area of magnetic poles of the suspension As we know, the existing results have focused mainly on the attenuation on external disturbances, fault tolerant, actuator failure and the manipulation on uncertain parameters [4,5]. However, the finite-time control is important due to its fast convergence and good robustness [6][7][8][9][10]. To the best of authors' knowledge, this issue has not been solved for the maglev system so far.…”