时滞广义正系统的性能分析与控制

Positive descriptor time-delay systems have been widely applied to biological models, economic models, network systems and so on. As the generalization of the positive time-delay systems, positive descriptor time-delay systems are complex differential and algebraic equations, whose performance analysis and feedback controller design haven't been fully understood. In this project, we will extend the results obtained in our previous work on bounded delays to the analysis of positive descriptor systems with unbounded delays and homogeneous positive descriptor systems. We will transform the descriptor time-delay system into a new augmented system and guarantee its equivalence with the original system. Then, the dynamic characteristics of the positive descriptor time-delay system are investigated for different input and output signal spaces, and the performance analysis with less conservatism is given. Ensuring the regularity and non-impulsiveness of the system, the synthesis problem of positive descriptor time-delay systems under different gain performances will also be analyzed and solved by a proposed algorithm. In addition, the theoretical results will be applied to the consensus analysis of networked time-delay multi-agent systems. The purpose of this project is to establish a set of novel approaches for the performance analysis and synthesis of positive descriptor time-delay systems in order to provide a theoretical basis for the engineering application.

时滞广义正系统在生物学模型、经济学模型、网络化系统等有着广泛的应用。作为时滞正系统的推广，时滞广义正系统是复杂的微分代数方程，其稳定性分析与反馈控制器设计难度大，增益性能分析与反馈控制理论欠缺。本项目计划将前期在有界时滞方面获得的成果，推广到无界时滞广义正系统以及齐次广义正系统的分析中；将时滞广义系统转化成新的增广系统，保证其与原系统等价。进而针对不同的输入输出信号空间，分析时滞广义正系统的动态特性，给出保守性较低的性能指标刻画；在保证系统的正则性和无脉冲性的基础上，设计不同增益性能下时滞广义正系统状态反馈和输出反馈控制器并给出求解算法；并且将以上理论结果应用于网络化时滞多智能体的一致性问题中。本项目拟建立完整的时滞广义正系统的性能分析与综合理论，为时滞广义正系统的工程应用奠定基础。

时滞广义正系统在生物学模型、经济学模型、网络化系统等有着广泛的应用。许多表示实际系统的动力系统模型都天然的带有非负约束，在仓室网络、基因网络、交通流量网络等系统中得到广泛的研究和应用。本项目将前期在有界时滞方面获得的成果，基于T-S模糊模型推广到无界时滞非线性广义正系统，并进一步应用推广到非线性齐次广义正系统的时滞稳定性分析中。通过将一类传播网络模型建模为齐次非线性广义系统，给出了传播过程收敛性分析。进而针对不同的输入输出信号空间，分析正系统的动态特性，给出保守性较低的L1/L-性能指标刻画，并应用于电力系统的故障诊断中。然后，深入研究并利用正系统理论处理网络系统的一致性分析与控制问题。基于几何规划方法，建立了正系统网络系统资源调度和分配优化方法。此外，针对无向图下的正系统和正系统网络存在参数不确定性问题，基于龙伯格观测器给出动态输出反馈鲁棒控制器设计方法，一方面考虑观测器和控制器的脆弱性，给出基于观测器的网络系统非脆弱控制方法。最后，本项目还基于正系统网络的研究结果，进一步针对有向图下的多智能体系统设计了给定时间分布式状态观测器和有限时间控制器。