切换线性系统的性能估计及其应用

项目名称： 切换线性系统的性能估计及其应用

项目编号： No.61273121

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 孙振东

作者单位： 华南理工大学

项目金额： 82万元

中文摘要： 切换线性系统解轨线的（紧）范数上界估计提供了系统性能的重要和丰富信息，包括刻画切换线性系统最大发散速率的Lyapunov指数和刻画临界化系统最大发散速率的（多项式）指数。本项目以探索切换线性系统的性能估计为目标，利用非方代数变换和平方和（SOS）技术寻求逼近系统Lyapunov指数的可执行算法，探索临界切换系统的同步化切换设计以寻求临界发散指数的估计。有关结果可应用于几类多线性动态系统的稳定性分析，包括凸多面体微分包含系统的强稳定性，线性参数变化（LPV）系统的鲁棒稳定性，以及鲁里叶系统的绝对稳定性，预期可获得相关稳定性的（非保守）判据及在算法意义上的可验证判据。对一类具有侧面电极的微机电扭转微镜，拟将有关理论结果应用于下拉动态分析，目标是优化微镜的稳定运动范围。拟解决的关键科学问题包括①矩阵集极小公共测度的逼近；②临界块三角系统的同步最大发散切换设计；③扭转微镜的下拉动态优化。

中文关键词： 切换系统；性能分析；多线性进程系统；矩阵集测度；MEMS扭转微镜

英文摘要： Tight upper bound estimation of the trajectory norm for switched linear systems provides important and rich information on system performance, which includes the top Lyapunov exponent that characterizes the largest divergence rate of the trajectories and the largest polynomial order of divergence for marginalized switched systems. Aiming to investigate the performance estimate of switched linear systems, the project seeks tractable computational algorithms to estimate the Lyapunov exponent by using either the non-square algebraic transformation method or the sum-of-squares technique, and estimates the marginalized divergence order by means of synchronized switching design for marginal switched systems. The performance estimate could be used to stability analysis for several frameworks of multi-linear processes including strong stability of polyhedron differential inclusions, robust stability of linear parameter-varying systems, and absolute stability of Lur'e systems. Verifiable and non-conservative criteria could be deducted along this line. For a class of MEMS torsional micromirror systems with side electrode, we are to apply the theoretical analysis into the optimization of the pull-in dynamics to broaden the stable motion scope. The key scientific problems to be addressed in the project include i) Approximat

英文关键词： Switched systems；Performance analysis；Multi-linear dynamical systems；Matrix set measure；MEMS torsional mirror