Impulsive systems with hybrid delayed impulses: Input-to-state stability

This paper investigates input-to-state stability (ISS) and integral-input-to-state stability (iISS) of nonlinear impulsive systems with hybrid delayed impulses. Based on Lyapunov method, some sufficient conditions ensuring ISS and iISS of impulsive systems are obtained, where the time derivative of Lyapunov function is indefinite, and the hybrid effects of delayed impulses are also fully considered. It is shown that the impulsive system is ISS provided that the combined action of time delay existing in impulses, continuous dynamic, and the cumulative strength of hybrid impulses satisfies some conditions, even if the hybrid delayed impulses play a destabilizing effect on ISS. Examples and their simulations are presented to illustrate the applicability of the proposed results.     

Robust H∞ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then,a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.     

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

New approach to differential equations with countable impulses

This paper provides a new approach to study the solutions of a class of generalized Jacobi equations associated with the linearization of certain singular flows on Riemannian manifolds with dimension n + 1.A new class of generalized differential operators is defined.We investigate the kernel of the corresponding maximal operators by applying operator theory.It is shown that all nontrivial solutions to the generalized Jacobi equation are hyperbolic,in which there are n dimension solutions with exponential...     

PERSISTENCE AND PERIODIC SOLUTIONS FOR NONAUTONOMOUS PREDATOR-PREY SYSTEM WITH IMPULSES

In this paper, a nonautonomous Predator-prey model with functional response and impulses is studied. By using comparison theorem and the mono-tonicity, some sufficient conditions which guarantee the permanence and asymptotic behavior of this system are obtained.     

Periodic Duffing delay equations with state dependent impulses

Conditions are obtained for the Duffing equation with delay and state dependent impulses to admit a periodic solution.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

随机脉冲泛函微分方程的{\boldmath p}阶矩有界性

随机脉冲泛函微分方程是一个具有广泛应用前景的数学模型. 该文利用带Razumikhin条件的Liapunov直接法和比较原理, 得到了随机脉冲泛函微分方程的解的一致(一致且最终、一致且一致最终) p阶矩有界的充分条件, 其中在获得一致有界性和一致最终有界性时, 对dV(t, x(t))/dt 的限制条件也较少, 因此研究结果非常便于应用.     

高等数学的阅读能力培养初探

认识高等数学阅读能力的重要性、激发大学生对高数学阅读的兴趣、提供数学阅读的具体方法是培养高等数学阅读能力的措施.其中,数学阅读的具体方法有:带有问题阅读、督促学生作读书笔记、个别指导、组织课堂讨论和经验交流、及时小结、合理评价等.高等数学教师应该努力探寻提高大学生数学阅读能力的有效方法.