Practical stabilization of control systems with impulse effects

AbstractIn this paper, we investigate practical stabilization of control systems with impulse effects. Utilizing piecewise continuous Lyapunov functions and impulsive differential inequalities, we prove some general comparison results through which we establish some sufficient conditions for practical stabilization of control systems with impulse effects. We also use two different measures, which gives a unified approach, and include many interesting special cases

Difficulties of College Students’ Business Startups Under Economic New Normal and Their Countermeasures

The economic new normal has become a necessary stage of China’s economic development. In order to promote effective business startups of college students under economic new normal, research on influences of economic new normal on college students’ business startups and main difficulties faced by college students during business startups under economic new normal was carried out. Findings of research: The economic new normal generated more needs of business startups, needed more entrepreneurship participation of college students and required impressive promotion of the entrepreneurship efficiency. However, the present entrepreneurship environment cannot satisfy urgent needs of college students’ business startups. What’s more, factors such as lack of entrepreneurship capital, insufficient education on college entrepreneurship, low entrepreneurship quality of college students and social prejudice seriously impeded the development of college students’ business startups. Hence, support of college students’ business startups should be strengthened in aspects of entrepreneurship environment optimization, fund-raising channel innovation for entrepreneurship, innovation of the college entrepreneurship education system and social support etc.

Exponential stability for impulsive delay differential equations by Razumikhin method

AbstractIn this paper, we study exponential stability for impulsive delay differential equation of the form x˙(t)=f(t,xt),t≠tk,Δx(t)=Ik(t,xt−),t=tk,k∈N. By employing the Razumikhin technique and Lyapunov functions, several exponential stability criteria are established. Some examples are also discussed to illustrate our results

Stability and robustness of quasi-linear impulsive hybrid systems

AbstractBoth hybrid dynamical systems and impulsive dynamical systems are studied extensively in the literature. However, impulsive hybrid systems are not yet well studied. Nonetheless, many physical systems exhibit both system switching and impulsive jump phenomena. This paper investigates stability and robust stability of a class of quasi-linear impulsive hybrid systems by using the methods of Lyapunov functions and Riccati inequalities. Sufficient conditions for stability and robust stability of those systems are established. Some examples are given to illustrate the applicability of our results

Study of singular boundary value problems for second order impulsive differential equations

AbstractThis paper studies the existence of extremal solutions for a class of singular boundary value problems of second order impulsive differential equations. By using the method of upper and lower solutions and the monotone iterative technique, criteria of the existence of extremal solutions are established

Impulsive stabilization of stochastic functional differential equations

AbstractThis paper investigates impulsive stabilization of stochastic delay differential equations. Both moment and almost sure exponential stability criteria are established using the Lyapunov–Razumikhin method. It is shown that an unstable stochastic delay system can be successfully stabilized by impulses. The results can be easily applied to stochastic systems with arbitrarily large delays. An example with its numerical simulation is presented to illustrate the main results

Absolute stability of lurie systems with impulsive effects

AbstractThis paper studies absolute stability of Lurie systems with impulsive effects. Using the method of Lyapunov functions and the variation of parameters technique, we establish sufficient conditions for absolute stability