Asymptotic stability of solutions of impulsive multi-delay differential equations

作者：You, Zhongli; Wang, JinRong^*; O'Regan, D.

来源：TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2018, 40(15): 4143-4152.

DOI：10.1177/0142331217742966

• Impulsive differential equations
• multiple delays
• impulsive multi-delayed Cauchy matrix
• solution
• asymptotic stability

In this paper, we consider the asymptotic stability of solutions to impulsive multi-delayed differential equations with linear parts defined by pairwise permutable matrices. First, we introduce the concept for an impulsive multi-delayed Cauchy matrix and then use it to obtain the representation of solutions to linear impulsive Cauchy problems via the variation of constants principle. Next, we give a norm estimate of the impulsive multi-delayed Cauchy matrix and establish sufficient conditions to guarantee that the trivial solutions are asymptotically stable when the nonlinear terms satisfy appropriate conditions. Finally, two numerical examples are given to illustrate the effectiveness of the results.

• 出版日期2018-11
• 单位贵州大学