This study investigates the semi-global fixed-time stability (SGFTS) and global fixed-time stability (GFTS) of nonlinear impulsive systems (NISs). A key challenge in analyzing the SGFTS of such systems lies in the evolving integration methods caused by the impulses. To address this, we dynamically partition the semi-global attraction set (SGAS) and solve the corresponding differential equations within each subset. Additionally, by constructing the transition dynamics of impulse points and iteratively computing these points, we establish the conditions for SGFTS under both stabilizing and destabilizing impulses. For GFTS, the primary difficulty arises from the distinct trajectories and dynamics of points located inside and outside the SGAS. To overcome this, we introduce the concept of the maximum-minimum impulse interval and derive a sufficient condition that ensures the system can enter the SGAS from a distance under a finite number of impulses. Furthermore, we develop a criterion for GFTS under varying impulse degrees and provide convergence time estimation based on the research on SGFTS of NIS. Finally, numerical examples are presented to validate the theoretical results. Notably, in Example 3, a fixed-time impulse controller is designed based on the proposed theoretical framework to achieve global stabilization of complex systems. This example highlights the potential applications of this work in the field of control.

This article focuses on achieving the finite-time synchronization (FTS) for fractional complex dynamical networks (FCDNs) using hybrid impulsive control. Initially, a novel framework for local FTS is developed, building upon the relaxed inequality${}_{{t_{k}}}^{C}D_{t}^{{\alpha}}V( t ) \le \chi V( t ) - \eta$. To expand the attraction domain within the local FTS framework, a piecewise fractional-order differential inequality based on impulsive control systems is proposed. Subsequently, a new hybrid control strategy is designed by integrating a simple feedback controller with an impulsive controller involving a finite number of impulses, which can be accurately calculated using the proposed impulsive degree. Additionally, a set of local/global FTS criteria is formulated, and the settling time can be explicitly estimated. Lastly, an illustrative example is presented to demonstrate the effectiveness of the derived results.

In this contribution, the problem of fixed-time stabilization in multi-weighted complex networks via the novel adaptive pinning nonchattering control based on the linear matrix inequality (LMI) method, as well as its application to image protection is addressed. Different from the traditional methods, a novel fixed-time stable form is proposed and the convergence time is estimated based on beta function. Next, utilizing the designed continuous adaptive control strategy, a sufficient LMI condition is presented to ensure the fixed-time stabilization of multi-weighted complex networks. Furthermore, the novel nonchattering adaptive pinning control protocol is given to guarantee the fixed-time stabilization of the system only by controlling a small number of nodes. Note that a scheme of how to select the number of control nodes is put forward accordingly. Finally, the effectiveness of the proposed method is verified by the actual financial model. Meanwhile, a number of encryption experiments are carried out based on three networks, and the mean and variance of the encryption performance are calculated to show the stability and robustness of image encryption different from the existing research works.

This work explores the fixed-time stabilization of fuzzy uncertain systems based on conditional integral sliding mode control. The difficulties in solving such problems include the integral windup problem and the severe chattering problem when the system converges. Moreover, the design of the traditional fixed-time controller algorithm in the integral sliding mode control becomes complicated. In order to overcome these difficulties: 1) a piecewise function which can bring distant states closer to the sliding surface is considered in the integral function to prevent the integral windup problem, 2) a class of state variable controllers with odd power is designed to solve the chattering problem due to there is no sign function, 3) a fixed-time control algorithm is introduced into the integral function and the controller to guarantee that both the reachability and sliding motion phases are fixed-time stable. Furthermore, based on 1) and 3), an appropriate fixed-time conditional integral sliding mode controller is constructed to ensure the fixed-time reachability of the designed sliding mode surface. Besides, combining 1), 2) and 3), a class of chattering-free fixed-time integral sliding-mode controllers is established to obtain the fixed-time reachability of the sliding mode surface and the fixed-time stability of sliding mode dynamics. This method dramatically reduces the chattering problem and can adjust integral windup. Finally, two numerical simulations are presented to verify the theoretical results, showing the robustness of the designed overshoot factor and the chattering-free scheme for sliding mode control.

This article mainly explores the fixed-time control problem of fuzzy semi-Markov systems with uncertainties and unknown transition rates. Firstly, the T-S fuzzy semi-Markov system is established by using the membership relation of fuzzy logic and Markov probability property. Then, unlike the existing fixed-time control strategies, this work uses a hyperbolic sine function to replace the traditional multiple powers fixed-time control method and construct a novel fixed-time adaptive integral sliding mode control strategy, which reduces the complexity of the controller and adaptive law while optimizing the sliding mode surface and improving the fixed-time convergence performance of the system. Moreover, compared with current methods that require the assumption that the unknown function satisfies the Lipschitz condition or is bounded, the fully connected neural network is introduced to approximate the unknown nonlinear function in the system, improving the intelligence and practicality of the controller. Finally, the theoretical results are verified through numerical simulation, showing the superior performance of achieving fixed-time stability through the proposed control scheme, the gap in the study of fixed-time control using hyperbolic sine functions and fully connected neural networks is filled.

This article investigates fixed-time stabilization of fuzzy neural networks with distributed delay by designing an adaptive sliding mode controller. First, according to stability theory and related inequalities, a new fixed-time stability theorem is put forward, and the settling time is given. In order to stabilize the system, a new integral sliding mode surface is designed, and the corresponding sliding mode control strategy and adaptive sliding mode control strategy are established. Some criteria that can be obtained, and it is shown that the neuronal states of neural networks will arrive at the sliding surface in a fixed time, and then approach zero along the sliding surface. Compared with existing sliding mode control techniques, this work extends the previous related results by choosing different parameters of the controller and the sliding mode manifold to gain various protocols. Finally, two examples are provided to verify the validity of the theorems in this work.