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| Impulse control of functional differential equations |
| FENG Wei-zhen, LI Shao-e |
| School of Math. Sci., South China Normal Univ., Guangzhou 510631, China |
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Abstract This paper investigates the impulse control of functional differential equations with the general form of $\dot{x}(t)=f(t, x(t), x(t-r))$. By employing comparison theorems, it proves that if $f$ is continuous, the boundness or attractiveness of the solutions can be obtained by impulse control, and if $f$ satisfies the weak Lipschitz Conditions, the equations can be stablized, asymptotically stablized or exponentially stablized by impulse control, and the algorithm of impulse control is provided.
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Received: 24 December 2013
Published: 29 July 2018
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泛函微分系统的脉冲控制
考察了较为一般形式的泛函微分系统 $\dot{x}(t)=f(t,x(t),x(t-r))$的脉冲控制问题. 通过使用比较定理得到了系统在解存在唯一及 $f(t,x,y)$连续的前提下, 即可脉冲控制有界, 吸引的结论; 在弱利普希茨条件下, 得到可脉冲控制稳定, 渐近稳定及指数稳定的结论, 并得到了脉冲控制的具体算法.
关键词：
脉冲微分系统,
泛函微分方程,
可脉冲控制
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