一种估计奇异摄动饱和系统稳定域的方法  

A Method for Estimating the Stability Region of Singular Perturbation Systems with Saturation Nonlinearities

作　　者：辛焕海[1] 吴荻[1] 甘德强[1] 邱家驹[1] 

机构地区：[1]浙江大学电气学院电机系,杭州310027

出　　处：《自动化学报》2008年第12期1549-1555,共7页Acta Automatica Sinica

基　　金：国家自然科学基金(50595411;50807046);教育部新世纪人才计划(NCET-04-0529);中国博士后基金(20070420224)资助~~

摘　　要：针对奇异摄动饱和系统,提出了一种估计其稳定域的降阶方法。结合饱和函数的特殊性质,证明了此类系统的稳定域可分解为伴随系统的不变集与一个足够大球体的笛卡尔积,将原系统稳定域估计问题转化为低阶伴随系统稳定域的估计问题,利用线性矩阵不等式(Linear matrix inequality,LMI)优化方法估计伴随系统的稳定域以减少保守性。本方法不仅可以克服奇异摄动饱和系统的奇异性,还可以一定程度克服系统的"维数灾"等问题.A reduced-order method was proposed for estimating the stability region of singular perturbation dynamical systems with saturation nonlinearities. Based on the properties of the saturation function, it was proved that the stability region of such dynamical systems can be decomposed into Cartesian product of an invariant set of their adjoint systems and a sufficiently large ball. The stability region estimation of the singularly perturbed systems can be replaced by that of the adjoint systems, and an optimization method based on linear matrix inequality was provided to reduce the conservativeness in the estimation. The proposed method can eliminate the singularity and overcome the dimension disaster to some extent.

关 键 词：稳定域 奇异摄动系统 饱和非线性 线性矩阵不等式 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]