lyapunov function method
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Abstract In this paper, the global asymptotic stability (GAS) of continuous-time and discrete-time nonlinear impulsive switched positive systems (NISPS) are studied. For continuous-time and discrete-time NISPS, switching signals and impulse signals coexist. For both of these systems, using the multiple max-separable Lyapunov function method and average dwell-time (ADT) method, some sufficient conditions on GAS are given. Based on these, the GAS criteria are also given for continuous-time and discrete-time linear impulsive switched positive systems (LISPS). From our criteria, the stability of the systems can be judged directly from the characteristics of the system functions, switching signals and impulse signals of the systems. Finally, simulation examples verify the validity of the results.

In this work, since the importance of investigation of oscillators solutions, an methodology for proving the existence and stability of almost anti-periodic solutions of inertial neural networks model on time scales are discussed. By developing an approach based on differential inequality techniques coupled with Lyapunov function method. A numerical example is given for illustration.

The algebraic connectivity is crucial parameter in studying of synchronization of diffusively coupled networks. This paper studies the synchronization in networks of Hindmarsh-Rose systems, which is one of the most used neuron models. It presents sufficient condition for synchronization in these networks using the Lyapunov function method. This is a simple condition which depends on the algebraic connectivity and on the parameters of the individual system. Numerical examples are presented to illustrate the obtained results.

Emotion plays an important role in decision making. In an emergency, panic can spread among crowds through person-to-person communications and can cause harmful effects on society. The aim of this paper is to propose a new theoretical model in the context of epidemiology to describe the spread of panic under an emergency. First, according to divisions in personality in the context of psychology, groups are divided into a level-headed group and an impatient group. Second, individuals in the two groups have unique personalities. Thus, the level-headed group only infects within the group, while the impatient group considers emotional infection within the group and cross infection between the groups. Then, a nonlinear infection rate is used to describe the probability of infection after an infected person contacts a susceptible person, which is more in line with the real situation. After that, the level-headed group–impatient group nonlinear SIRS panic spreading model is developed. Stable analysis of the model is obtained using the Lyapunov function method to study the stability of the panic-free equilibrium and panic-permanence equilibrium. Finally, simulations are carried out to dynamically describe the spread process of group emotional contagion.

In this study, a deterministic SEQIR model with standard incidence and the corresponding stochastic epidemic model are explored. In the deterministic model, the reproduction number is given, and the local asymptotic stability of the equilibria is proved. When the reproduction number is less than unity, the disease-free equilibrium is locally asymptotically stable, whereas the endemic equilibrium is locally asymptotically stable in the case of a reproduction number greater than unity. A stochastic expansion based on a deterministic model is studied to explore the uncertainty of the spread of infectious diseases. Using the Lyapunov function method, the existence and uniqueness of a global positive solution are considered. Then, the extinction conditions of the epidemic and its asymptotic property around the endemic equilibrium are obtained. To demonstrate the application of this model, a case study based on COVID-19 epidemic data from France, Italy, and the UK is presented, together with numerical simulations using given parameters.

In this paper, outer synchronization of complex-variable networks with complex coupling is considered. Sufficient conditions for achieving outer synchronization using static impulsive pinning controllers are first derived according to the Lyapunov function method and stability theory of impulsive differential equations. From these conditions, the necessary impulsive gains and intervals for given networks can be easily calculated. Further, an adaptive strategy is introduced to design universal controllers and avoid repeated calculations for different networks. Notably, the estimation algorithms of the impulsive gains and intervals are provided. Finally, three numerical examples are performed to verify the effectiveness of the main results.

This paper focuses on autonomous underwater vehicle (AUV) stabilization in the nonlinear descriptor model, as well as some AUV limitations such as model uncertainty, singularity, saturation constraint, and time delay. The capability of the descriptor model to show the real model is more reasonable than the standard state-space model. Based on the constructed Lyapunov function method and applying the bilinear matrix inequalities technique, all of the constraints are handled by introducing the new theorem. This theorem aims to design a state feedback with the intent that the closed-loop system be admissible. Here, the results are less conservative than other approaches. This issue has not yet been fully addressed in the literature, especially on AUVs. Theorem achievement is implemented on new AUV descriptor model that is obtained and introduced here. This method covers both neutral and descriptor systems. Also, it can be generalized and applied to conventional AUVs or similar dynamics. Examples and simulation results illustrate the effectiveness of the proposed approach.