复系数时滞系统的动力学与控制研究

项目名称： 复系数时滞系统的动力学与控制研究

项目编号： No.11202187

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 李俊余

作者单位： 浙江海洋学院

项目金额： 26万元

中文摘要： 复系数时滞微分方程在光电系统、生物系统、转子系统及非线性时滞系统的数值分析和分岔分析中是基本而重要的数学模型。对这类系统的研究具有重要的实际意义和应用价值。 本项目针对这类系统作如下三个方面的研究：(1)建立可以直接分析系数和时滞相关的复系数时滞系统的稳定性切换方法。(2)针对研究非线性时滞系统时得到的系数和时滞相关的复系数振幅方程，在不对时滞项作近似处理的前提下研究它的分岔和复杂动力学现象。(3) Sename解耦控制有时会将实系数系统解耦为复系数时滞系统，针对这种情形给出控制参数的确定方法，并进一步给出当原系统含有不确定参数时的鲁棒控制方法。 本项目的研究成果可为工程实践提供理论指导，同时由于复系数时滞系统与实系数时滞系统在研究方法和动力学特性方面存在诸多差异，本项目的开展还具有重要的学术意义。

中文关键词： 时滞微分方程；渐近稳定；时滞反馈；镇定；

英文摘要： Delay differential equations with complex coefficients (complex-DDEs) serve as basic and important mathematical models in laser systems, biological systems and rotor systems. They also play important roles in numerical analysis and bifurcation analysis in nonlinear systems with time delay. Therefore, carrying out research work on this type of systems has important theoretical value and wide applications. This project mainly includes the following three aspects: (1) To present a method for analyzing the stability of complex-DDEs directly on the basis of stability switch. (2) The amplitude-frequency equation of a nonlinear oscillator with delay feedback is always a delay differential equation with delay-dependent coefficients. A Hopf bifurcation analysis and complex dynamic analysis of this type of systems will be given without approximating the time delay system as an ordinary differential equation. (3) To determine the control parameters when a system with real coefficients is transformed into complex-DDEs by using Sename decoupling control method. Further to give the method for the robust control of the unstable systems with uncertain parameters. The achivements of this project offer some theoretical guidanc for engineering practice. In addition, this project has important academic significance since the

英文关键词： Delay differential equation；Asymptotical stability；Time delay feedback；Stabilization；