时滞广义正系统的性能分析与控制

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。

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.