Guizhen Feng’s research while affiliated with Nanjing Institute of Industry Technology and other places

This article explores the criteria for fixed‐time stability (FxTS) within nonlinear impulsive dynamical systems, encompassing both stabilizing and destabilizing impulses. Initially, employing the Lyapunov method, the article delineates a criterion for FxTS, particularly when impulsive sequences are delineated by an average impulsive interval. Following this, the article innovatively applies two integral inequalities to introduce an optimized criterion for uniform impulsive sequences, evidencing its lesser conservativeness relative to the initial criterion. Moreover, this article derives a necessary condition for dynamical systems subjected to destabilizing impulses. Intriguingly, the investigation reveals the existence of a minimal threshold for the maximum impulsive interval, below which the system cannot achieve FxTS. This result elucidates why existing literature uniformly imposes a specific condition on the impulsive interval for destabilizing impulses. Finally, the efficacy of the proposed theory is underscored through numerical examples.

This study investigates the bipartite synchronization of heterogeneous signed networks with distributed impulsive control. Leader-follower bipartite synchronization within a nonzero error bound is analyzed when the average impulsive interval is Ta<∞ or Ta=∞. Some sufficient conditions to achieve the bipartite quasi-synchronization are presented, and the synchronization error level is estimated by the specific mathematical expression. The correctness of the theoretical results is verified by numerical examples.

This work focuses on exponential synchronization for a class of partially coupled heterogeneous networks with time-delays and heterogeneous impulses. The synchronization targets are selected as the common equilibrium solution and the average trajectory, respectively. Some synchronization criteria are deduced by using Lyapunov function and comparison principle.

This paper investigates exponential stability of nonlinear delayed impulsive systems. The effects of impulses with sufficiently small input delays and arbitrary sizes of input delays are thoroughly examined according to whether the continuous dynamics of the systems is stable. Several exponential stability criteria are obtained and are then applied to study constant time-delay systems with linear input impulses. Numerical examples are provided to illustrate the usefulness of the main study results.

This paper concerns globally exponential synchronization for a class of impulsive networks with time-delays. The strategy is based on pinning control: single controller is designed to pin the whole network and realize synchronization. Some new conditions are imposed on impulsive sequences, which makes the results obtained in this paper less conservative. A numerical example is supplied to illustrate the validity of the main results.

This study investigates the exponential stability problems of singular impulsive switched systems. Using the switched Lyapunov function method and algebraic inequality, sufficient conditions are expressed as arbitrary and conditioned impulsive switching has been obtained. In addition, with the introduction of the impulsive controller, several exponential stability criteria are derived when the impulsive controllers are stabilising. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.

By employing Lyapunov functional method and linear matrix inequalities (LMIs), the asymptotical stability is studied for the coupled delayed neural networks. Furthermore, we presented a new neural network model including both intrinsic disturbance of single node and communication noise over the network connections. Only one controller is used for the stabilization of the neural networks in terms of LMIs, and the prescribed L2-gain condition is satisfied. The proposed linear matrix inequality results are easy to be solved by standard commercial software. An illustrative example is given to show the effectiveness of the result.

This paper concerns time-delay systems with delayed impulses. Average impulsive intervals is used to replace the lower and upper bounds of impulsive intervals, which weakens the limitations to the impulsive sequences. Under some modified conditions on the impulsive functions and the Lyapunov-based function, the exponential stability of systems is established. A specific impulsive delayed system with linear input time-delays is investigated by virtue of the obtained results. Finally, some numerical example is given to demonstrate the applicability of our results.