溢出非线性二维数字滤波器系统的稳定性研究

项目名称： 溢出非线性二维数字滤波器系统的稳定性研究

项目编号： No.61473135

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 申涛

作者单位： 济南大学

项目金额： 85万元

中文摘要： 本申请旨在降低溢出非线性二维(2-D)滤波器系统稳定性分析的保守性，利用全局吸引集方法、状态分区方法和分段Lyapunov函数方法，研究溢出非线性2-D系统的稳定性问题，提出新的稳定充分条件。根据全局吸引集的估计结果，能够排除部分溢出非线性发生的可能性，降低系统的复杂程度；采用状态分区和分段Lyapunov函数方法能够减小稳定性分析的保守性。二维系统与一维(1-D)系统存在显著差异，将1-D系统的相关结果直接应用于2-D系统，很难获得良好的效果。因此，针对溢出非线性2-D系统的特点，研究全局吸引集估计方法、状态分区方法和分段Lyapunov函数构造方法既是本申请的创新之处也是必须要解决的关键问题。本申请前期研究了1-D系统的全局吸引集方法、状态分区方法和分段Lyapunov函数方法，并取得了部分研究成果，这为本申请的研究提供了必要的研究基础，同时本申请也是前期研究工作的自然延续。

中文关键词： 稳定性；溢出；分段Lyapunov函数；全局吸引集；状态分区

英文摘要： The aim of this application is to reduce the conservatism in the stability analysis for two-dimensional(2-D)system with overflow nonlinearities. The stability of these systems will be studied by by estimating globally attractive set, partitioning state's region and constructing the piece-wise Lyapunov function. Some overflow nonlinearities may be ruled out by estimating global attractive sets. And then, the complexity of these systems may be reduced. The conservatism in the stability analysis for these systems can be reduced by partitioning state's region and constructing the piece-wise Lyapunov function. There are significant differences between 2-D systems and one-dimensial(1-D)systems. So, it is difficult to obtain satisfactory results by directly using the results about 1-D systems to 2-D systems. It is the Innovation and key problem to study the method of estimating globally attractive set, partitioning state's region and constructing the piece-wise Lyapunov function according to the character of 2-D systems. These methods about 1-D systems have been studied. This provides the necessary research foundation for this application. And this application is also a continuation of the previous research work.

英文关键词： stability;overflow;piecewise Lyapunov function;global attractive set;state partition