正切换多时滞脉冲系统的分析与控制研究

The dynamic behavior of many practical systems, such as data communication networks, can be described by positive switched systems. The theoretical analysis and control research of this kind of system is one of the hot topic in the filed of control science. In view of the fact that time delays and impulses are the main factors affecting the performance of positive switched systems, this project study the analysis and control of positive switched systems with mixed time delays and impulses by using an improved copositive Lyapunov-Krasovskii functional method. Firstly, for the case where the growth rate of time-varying delay is greater than 1, the criteria of asymptotic stability of the considered systems are given by constructing improved copositive Lyapunov-Krasovskii functionals and introducing appropriate parameters and transformations. Secondly, when partial or all subsystems are unstable, by limiting the relationship between switching times, the total dwell time of stable (unstable) subsystems and impulse, or using the idea of discrete Lyapunov function, the sufficient conditions of dwell time switching stabilization for the considered systems are provided. Finally, considering that time-varying delay exists in both state and control input, the controller design schemes of stabilizable systems are given by designing reasonable feedback control, switching control and impulse control.This project will improve the existing methods only for the case of constant delay or growth rate of time-varying delay less than 1, and provide a complete theoretical analysis system for a wider type of positive switched systems. Therefore, this project has important research significance.

数据通信网络等很多实际系统的动态行为都可以描述为正切换系统。对这类系统的分析与控制研究，已成为当前控制科学领域的热点课题。鉴于时滞和脉冲是影响正切换系统性态的主要因素，本项目拟运用改进的余正Lyapunov-Krasovskii（L-K）泛函方法研究正切换多时滞脉冲系统的分析与控制问题。首先，考虑时滞增长率大于1，通过构造改进的余正L-K泛函，引入恰当的参数和变换，得到系统渐近稳定的判定准则。其次，通过限定切换次数、（不）稳定子系统总驻留时间以及脉冲之间的关系或者运用离散化Lyapunov函数思想，给出系统的驻留时间切换镇定设计方法。最后，考虑时滞同时存在于状态和控制输入中，通过设计合理的反馈控制、切换控制和脉冲控制，给出可镇定系统的控制设计方案。本项目将改进现有方法仅适用于常时滞或时滞增长率小于1的情形，为更广泛类型的正切换系统提供一套完整的理论分析体系。因此，本项目具有重要的研究意义。

切换信号的复杂多变、时滞形态的多样化和脉冲等现象普遍存在实际生产生活中，这使得正切换系统稳定性问题迫切需要解决。本项目研究了正切换时滞脉冲系统的稳定分析与控制设计问题。首先，构造了新型的多重余正李雅普诺夫-克拉索夫斯基泛函，弱化了对共同线性余正李雅普诺夫函数存在性的限制，大大降低了保守性；其次，利用平均驻留时间、引入参变量、线性矩阵不等式、离散化能量函数等技巧给出了所考虑系统指数稳定的判定准则；最后，通过设计合理的切换律或者控制策略，给出了部分子系统甚至所有子系统都不稳定时系统的多种镇定方案与控制算法。经仿真模拟验证，本项目提出的稳定性判定准则简洁且便于计算，给出的镇定方案与控制策略可执行度强，镇定效果好。本项目改进了已有的研究方法，为更广泛类型的正切换时滞系统提供了一套较为完整的理论分析体系，丰富了和发展了正切换系统控制设计方法。