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This paper delves into a comprehensive analysis of a generalized impulsive discrete reaction–diffusion system under periodic boundary conditions. It investigates the behavior of reactant concentrations through a model governed by partial differential equations (PDEs) incorporating both diffusion mechanisms and nonlinear interactions. By employing finite difference methods for discretization, this study retains the core dynamics of the continuous model, extending into a discrete framework with impulse moments and time delays. This approach facilitates the exploration of finite-time stability (FTS) and dynamic convergence of the error system, offering robust insights into the conditions necessary for achieving equilibrium states. Numerical simulations are presented, focusing on the Lengyel–Epstein (LE) and Degn–Harrison (DH) models, which, respectively, represent the chlorite–iodide–malonic acid (CIMA) reaction and bacterial respiration in Klebsiella. Stability analysis is conducted using Matlab’s LMI toolbox, confirming FTS at equilibrium under specific conditions. The simulations showcase the capacity of the discrete model to emulate continuous dynamics, providing a validated computational approach to studying reaction-diffusion systems in chemical and biological contexts. This research underscores the utility of impulsive discrete reaction-diffusion models for capturing complex diffusion–reaction interactions and advancing applications in reaction kinetics and biological systems.

In the field of the widely used helicopter, this paper studies whether the helicopters with three-degree freedom (3DOF helicopters) have a new control method of stable attitude. Therefore, two research methods are adopted. One is to use intermittent control, so as to achieve control stability in a short time without its inputting. The other is to find and update the time needed to meet the next control through the event-triggered mechanism. A theorem is given to prove the feasibility of these methods, and Lyapunov’s second law is also applied in this paper to analyze the stability of the model designed for robust attitude control. Besides, we use the linear matrix inequality solver to solve the feedback gain of the controller in the theorem. Finally, through MATLAB simulation, the system error state of helicopters tends to zero under intermittent control, which highlights the advantages of short communication time and few times of simulation, thus achieving the simulation goal.

In this paper, a new stability criterion of time-delay analysis is established for active controlled structure system. Based on an improved upper bound for the inner product of two vectors, the maximal value of time delay can be obtained by using LMI control toolbox of Matlab. According to the new method, the maximal delay varying with parameters of controlled structure system is discussed for SDOF system. The criterion is applicable to the theoretical analysis for the delay-dependent stability of SDOF vibrating system. The longer the delay is the worse the efficiency of control strategy. But the system is still asymptotically stable so long as the time-delay lies in the interval of permitted time delay.