The interest in non-linear impulsive systems (NIS) has been growing due to its impact in application problems such as disease treatments (diabetes, HIV, influenza, among many others), where the control action (drug administration) is given by short-duration pulses followed by time periods of null values. Within this framework the concept of equilibrium needs to be extended (redefined) to allows the system to keep orbiting (between two consecutive pulses) in some state space regions out of the origin, according to usual objectives of most real applications. Although such regions can be characterized by means of a discrete-time system obtained by sampling the NIS at the impulsive times, no agreements have reached about their asymptotic stability (AS). This paper studies the asymptotic stability of control equilibrium orbits for NSI, based on the underlying discrete time system, in order to establish the conditions under which the AS for the latter leads to the AS for the former. Furthermore, based on the latter AS characterization, an impulsive Model Predictive Control (i-MPC) that feasibly stabilizes the non-linear impulsive system is presented. Finally, the proposed stable MPC is applied to two control problems of interest: the intravenous bolus administration of Lithium and the administration of antiretrovirals for HIV treatments.

中文翻译：

---

非线性脉冲控制系统非零设定点的稳定性

由于非线性冲动系统（NIS）对诸如疾病治疗（糖尿病，HIV，流感等许多疾病）等应用问题的影响，对非线性冲动系统的兴趣日益增长，在这种情况下，控制措施（药物管理）是通过短时干预来实现的。持续时间脉冲，然后是空值的时间段。在此框架内，根据大多数实际应用的通常目标，需要扩展（重新定义）平衡的概念，以允许系统将某些状态空间区域中的轨道（在两个连续脉冲之间）保持在原点之外。尽管可以通过在脉冲时间对NIS进行采样获得的离散时间系统来表征这些区域，但是关于它们的渐近稳定性（AS）尚未达成任何协议。本文研究了NSI的控制平衡轨道的渐近稳定性，基于潜在的离散时间系统，以建立条件，后者的AS会导致前者的AS。此外，基于后一种AS表征，提出了一种可行的稳定非线性脉冲系统的脉冲模型预测控制（i-MPC）。最后，将拟议的稳定MPC应用于感兴趣的两个控制问题：锂的静脉推注给药和HIV治疗的抗逆转录病毒药的给药。